3rsity 
>uthern 
.ibrary  F 


THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


t  RALPH  D.  REED  LIBRARY 


DEPARTMENT  OF  GEOLOGY 

UNIVERSITY  of  CALIFORNIA 
LOS  ANGELES,  CALIF. 


D.    Trace 


O  0 


GEOLOGICAL  LIBRARY  OF 
ROBERT  DENNY  TRACE 

MAR  8   1941 


\frontispiece.] 


PLATE  I.— SUKVKYING  UNDER  DIFFICULTIES. 


TOPOGRAPHIC  SURVEYING. 


INCLUDING 


GEOGRAPHIC,  EXPLORATORY,   AND 
MILITARY   MAPPING, 


WITH    HINTS    ON 


CAMPING,  EMERGENCY  SURGERY,  AND 
PHOTOGRAPHY. 


BY 


HERBERT    M.   WILSON, 

Geographer,  United  States  Geological  Survey  ;  Member  American  Society  of 
Civil  Engineers  ;  Autiior  of  "Irrigation  Engineering"  etc. 


SECOND   EDITION,    REVISED. 
FIRST    THOUSAND. 


NEW    YORK: 

JOHN    WILEY    &    SONS. 

LONDON:    CHAPMAN   &   HALL,   LIMITED. 

1905. 


Copyright,  1900,  1905, 

BY 
HERBERT   M.  WILSON. 


ROBERT   DRUMMOND.    PRINTER.    NEW    YORK. 


Geology 
Library 

TA 


PREFACE. 


THIS  book  has  been  prepared  with  a  view  of  bringing 
together  in  one  volume  the  data  essential  to  a  comprehensive 
knowledge  of  topographic  surveying.  It  has  been  my  aim 
to  cover  the  varied  phases  of  all  classes  of  surveys  which  are 
made  with  a  view  to  representing  on  maps  information  rela- 
tive to  the  features  of  the  earth's  surface.  The  methods 
elaborated  are  chiefly  those  which  have  been  developed  in 
recent  years  by  the  great  government  surveying  organiza- 
tions and  by  such  few  private  corporations  as  have  kept  in 
touch  with  the  most  modern  practice;  but  I  have  endeavored 
to  go  beyond  these,  and,  guided  by  personal  experience,  to , 
adapt  them  to  the  most  detailed  topographic  as  well  as  to 
the  crudest  exploratory  surveys.  The  hope  is  entertained, 
therefore,  that  the  engineer  who  may  be  called  upon  to  con- 
duct an  exploratory  survey  in  an  unknown  region,  or  to  make 
a  detailed  topographic  map  as  a  preliminary  to  construction, 
will  find  herein  descriptions  and  examples  of  the  methods  he 
should  employ,  the  essential  tables  for  the  computation  of 
his  results,  and  hints  which  will  guide  in  the  equipment  of  his 
party. 

I  have  sought  to  avoid  any  detailed  description  of  those 
instruments  or  methods  which  are  elaborated  in  works  on 
general  surveying.  The  volume  is  devoted  practically  to 
higher  surveying,  and  presupposes  a  knowledge  of  all  the 
more  elementary  branches.  At  the  same  time,  many  of  the 

iii 


691186 


iv  PKEFA  CE. 

subjects  treated  are  essentially  elementary,  and  these  are 
briefly  described,  in  order  that  all  the  facts  which  the  topog- 
rapher must  know  and  all  the  formulas  and  tables  which  he 
must  have  at  hand  in  the  field  may  be  brought  together.  An 
effort  has  been  made  to  present  the  subject  in  the  most  prac- 
tical form.  Accordingly,  care  has  been  taken  to  avoid  an 
elaboration  of  the  mathematical  processes  by  which  the  vari- 
ous formulas  have  been  derived,  as  they  are  to  be  found  in 
detail  in  several  well-known  treatises  to  which  textual  refer- 
ence is  made.  To  give  more  immediate  aid  to  the  working 
surveyor,  examples  of  the  various  computations  are  pre- 
sented, as  are  illustrations  of  the  instruments,  methods,  and 
resulting  maps  from  surveys  actually  executed. 

The  mode  of  presentation  is  not  that  usually  followed  in 
such  works.  Instead  of  describing  the  instruments  or  their 
uses  independently,  each  is  described  in  that  portion  of  the 
text  in  which  its  employment  in  field  surveying  is  most  prom- 
inently mentioned.  The  tables  are  not  brought  together  at 
the  end  of  the  volume,  but  each  is  placed  in  that  portion  of  the 
text  which  relates  to  its  use.  The  object  is  to  produce  a  handy 
reference-book  for  use  in  the  field,  as  well  as  a  text-book  for 
guidance  in  college  instruction.  It  is  believed  that,  by  this 
arrangement,  if  a  topographer  in  the  midst  of  his  field-work 
desires  information  on  a  special  point,  it  can  be  found,  with 
accompanying  examples  and  tables,  gathered  together  in  one 
chapter  or  clearly  indicated  by  cross-references.  Again,  the 
method  of  treatment  usually  followed  in  works  of  this  class 
consists  in,  first,  a  description  of  the  astronomic  methods  on 
which  general  map  surveys  must  be  based,  and  then  a  descrip- 
tion of  primary  triangulation  as  a  basis  for  the  detailed 
topographic  surveys  which  are  finally  described.  I  have  re- 
versed this  order  and  have  adopted  the  more  natural  method 
of  commencing  with  the  simplest  operations  and  advancing 
gradually  towards  the  most  complex  and  refined.  Each  sub- 
ject is  treated  in  the  same  manner.  It  is  believed  that  the 


PREFA  CE.  V 

work  has  thus  been  made  especially  useful  to  the  inexpert 
topographer  and  the  student. 

The  volume  consists,  in  fact,  of  three  separate  books  or 
treatises:  (i)  Topographic  Surveying,  (2)  Geodetic  Survey- 
ing, and  (3)  Practical  Astronomy.  The  first  has  been  sub- 
divided into  three  parts:  Plane  Surveying,  Hypsometric  Sur- 
veying, and  Map  Construction;  and  these  are  preceded  by  a 
preliminary  characterization  of  the  relations  existing  between 
topographic,  geographic,  and  exploratory  surveys.  This  latter 
distinction  is  essentially  arbitrary,  as  all  are  of  a  kind,  and 
differ  only  in  degree  of  detail  and  the  consequent  speed  and 
generalization  in  procuring  the  field  results.  The  general 
subject  of  Geodetic  Surveying  has  been  subdivided  into  Ter- 
restrial Geodesy  and  Astronomic  Geodesy,  and  the  treatment 
of  these  differs  but  slightly  in  method  of  arrangement  from 
that  usually  pursued.  Part  VII  is  devoted  to  such  practical 
hints  as  it  is  believed  will  essentially  aid  those  who  have  the 
organization  and  command  of  camping  parties. 

I  am  especially  indebted  to  the  courtesy  of  Professors 
Ira  O.  Baker,  J.  B.  Johnson,  and  John  F.  Hayford  for  the 
use  of  numerous  electrotypes  and  plates  from  their  well- 
known  works  on  surveying  and  geodesy;  and  to  the  Secre- 
tary of  the  American  Society  of  Civil  Engineers  for  electro- 
types of  illustrations  in  articles  by  me.  I  am  also  indebted  to 
Messrs.  W.  &  L.  E.  Gurley,  Young  &  Sons,  and  G.  N.  Saeg- 
muller  for  electrotypes  of  instruments  illustrated  in  their  cata- 
logues. I  have  used  freely  the  excellent  Manual  of  Topo- 
graphic Methods  of  the  U.  S.  Geological  Survey,  written  by 
Mr.  Henry  Gannett;  in  a  few  instances  I  have  copied  verba- 
tim examples  contained  therein,  and  I  desire  to  express  appre- 
ciation of  his  courtesy,  and  of  that  of  the  Director  of  the  U.  S. 
Geological  Survey  in  extending  this  privilege.  To  the  latter 
I  am  also  indebted  for  an  opportunity  to  procure  the  colored 
illustrations  published  herewith,  which  were  printed  from  the 
admirable  copper-plates  of  the  U.  S.  .Geological  Survey.  Spe- 


vi  PREfA  CE. 

cifications  and  several  illustrations  of  tents  and  other  camp 
equipage  were  obtained  through  the  courtesy  of  the  Quarter- 
master-General of  the  U.  S.  Army.  For  much  in  the  chapter 
on  Photography  I  am  indebted  to  Lieut.  Samuel  Reber's 
Manual  of  Photography  and  to  E.  Deville's  Photographic 
Surveying. 

Finally,  I  desire  to  express  appreciation  of  the  assistance 
I  have  received  in  editing  manuscript  and  proof  from  many 
coworkers  on  the  U.  S.  Geological  Survey,  more  particularly 
from  Messrs.  W.  J.  Peters,  S.  S.  Gannett,  and  E.  M.  Douglas 
on  the  subjects  of  geodesy  and  astronomy;  E.  C.  Barnard 
and  A.  H.  Thompson  on  topographic  surveying;  C.  Willard 
Hayes  and  G.  K.Gilbert  on  topographic  forms  and  definitions; 
N.  H.  Darton  on  photography;  and  to  Mr.  W.  Carvel  Hall 
for  assistance  in  reading  proof.  Two  lists  of  works  of  refer- 
ence are  published,  on  pages  490  and  809,  in  which  are  cited 
the  titles  of  all  those  works  to  which  the  reader  is  referred  for 
further  details.  From  nearly  all  of  these  some  example  or 
illustration  has  been  obtained. 

H.  M.  W. 
WASHINGTON,  D.  C,  Feb.  22,  1900. 


PREFACE  TO  SECOND  EDITION. 


IN  preparing  this  second  edition  no  radical  changes  have 
been  made  in  any  chapter.  Numerous  minor  changes  and 
corrections  have  been  made,  however,  chiefly  in  the  nature  of 
citations  of  new  practices  or  correction  of  old.  This  is  par- 
ticularly true  of  the  subject  of  Projections,  which  is  better  illus- 
trated, that  of  Precise  Leveling,  and  the  bringing  up  to  date  of 
tables  of  Polaris  Observations. 

H.  M.  W. 

WASHINGTON,  D.  C.,  Feb.  20,  1905. 


CONTENTS. 


PART   I. 

TOPOGRAPHIC,  GEOGRAPHIC,  AND  EXPLORATORY  SURVEYING. 
CHAPTER    I. 

KINDS   OF   MAP  SURVEYS. 

ART.  PAGE 

1.  Classes  of  Surveys i 

2.  Information    Surveys 3 

3.  Topographic  Surveys 4 

4.  Features  Shown  on  Topographic  Maps 5 

5.  Public  Uses  of  Topographic  Maps 6 

6.  Degree  of  Accuracy  Desirable  in  Topographic  Surveys 8 

7.  Instructions  Relative  to  Topographic  Field-work 12 

8.  Elements  of  a  Topographic  Survey 14 

CHAPTER   II. 

SURVEYING   FOR   SMALL-SCALE   OR   GENERAL   MAPS. 

9.  Methods    of    Topographic    Surveying 18 

10.  Geological  Survey  Method  of  Topographic  Surveying 20 

11.  Organization  of  Field  Survey 22 

12.  Surveying  Open  Country 23 

13.  Sketching  Open  Country 28 

14.  Surveying  Woodland  or  Plains 33 

15.  Sketching  Woodland  or  Plains 35 

16.  Control  from  Public  Land  Lines 36 

17.  Sketching  Over  Public  Land  Lines 37 

18.  Cost  of  Topographic   Surveys 40 

19.  The  Art   of  Topographic    Sketching 40 

20.  Optical   Illusions   in   Sketching  Topography 44 

vii 


CONTENTS. 


CHAPTER    III. 

SURVEYING  FOR   DETAILED   OR   SPECIAL  MAPS. 

ART.  PACK 

21.  Topography  for   Railway   Location 47 

22.  Detailed  Topographic  Surveys  for  Railway  Location 49 

23.  Topographic  Survey  for  Canal   Location 52 

24.  Surveys  for  Reservoirs 57 

25.  Survey  of  Dam  Site 58 

26.  City  Surveys 62 

27.  Cadastral  and  Topographic  City  Survey 64 

28.  Cost  of  Large-scale  Topographic  Surveys 67 

CHAPTER   IV. 

GEOGRAPHIC  AND  EXPLORATORY  SURVEYS. 

29.  Geographic  Surveys 68 

30.  Instrumental  Methods  Employed  in  Geographic  Surveys 69 

31.  Geographic    Maps 70 

32.  Features  Shown  on  Geographic  Maps 72 

33.  Geographic  Reports 73 

34.  Scale  and  Cost  of  Governmental  Geographic  Surveys 74 

35.  Exploratory    Surveys 76 

36.  Exploratory  and  Geographic  Surveys  Compared 77 

37.  Methods  and  Examples  of  Exploratory  Surveys 82 

CHAPTER   V. 

MILITARY  AND  CADASTRAL  SURVEYS. 

38.  Military  -Surveys 52 

39.  Military  Reconnaissance  with  Guide  Map , 95 

40.  Military  Reconnaissance  without  Guide  Map 95 

41.  Detailed  Military  Map ,          , .  IOo 

42.  Military   Siege   Maps t !Oi 

43-  Military  Sketches  and  Memoirs  IO2 

44-  Cadastral   Surveys IO<j 

CHAPTER  VI. 

TOPOGRAPHIC  FORMS. 

45.  Relations  of  Geology  to  Topography t>  IO8 

46.  Origin  and  Development  of  Topographic  Forms 109 

47.  Physiographic    Processes t>  IIO 

48.  Classification  of  Physiographic  Processes 


CONTENTS.  IX 

ART.  PAGE 

49.  Erosion,   Transportation,  and   Corrasion 113 

50.  Topographic   Forms 120 

51.  Classification  of  Topographic   Forms 122 

GLOSSARY   OF  TOPOGRAPHIC   FORMS 133 


PART  II. 

PLANE  AND   T ACHY  METRIC  SURVEYING. 
CHAPTER   VII. 

PLANE-TABLES   AND   ALIDADES. 

52.  Plane  and  Topographic  Surveying 146 

53.  Plane-table   Surveying 147 

54.  Reconnaissance  and  Execution  of  Plane-table  Triangulation 149 

55.  Tertiary  Triangulation  from  Topographic  Sketch  Points 151 

56.  Varieties    of    Plane-tables 152 

57.  Plane-table  Tripods  and  Boards 153 

58.  Plane-table    Movements 153 

59.  Telescopic    Alidades 157 

60.  Adjustments  of  Telescopic  Alidade 159 

61.  Gannett    Plane-table 160 

62.  Sight-alidades    161 

63.  Folding   Exploratory   Plane-table 163 

64.  Cavalry    Sketch-board 164 

CHAPTER  VIII. 

SCALES,   PLANE-TABLE   PAPER,   AND   PENCILS. 

65.  Special  Scales 167 

66.  Slide-rule   : 168 

67.  Using   the   Slide-rule 169 

68.  Plane-table    Paper 174 

69.  Preparation  of  Field  Sheets 175 

70.  Manipulation  of  Pencil  and  Straightedge 178 

71.  Needle  Points,  Pencil  Holders  and  Sharpeners 179 

CHAPTER    IX. 

PLANE-TABLE    TRIANGULATION. 

72.  Setting  up  the   Plane-table 180 

73.  Location  by  Intersection 182 


CONTENTS. 


PAG 


ART. 

74.  Location  by   Resection  ........................................  185 

75.  Three-point  Problem   Graphically  Solved  ......................  186 

76.  Tracing-paper  Solution  of  the  Three-point  Problem  ............  187 

77.  Bessel's  Solution  of  the  Three-point  Problem  .................  188 

78.  Coast  Survey  Solution  of  the  Three-point  Problem  ............  190 

79.  Ranging-in,  Lining-in,  and  Two-point  Problem  ...............  192 

CHAPTER    X. 

TRAVERSE   INSTRUMENTS   AND   METHODS. 

80.  Traverse  Surveys  ..............................................   195 

81.  Traversing  by  Plane-table  and  Magnetic  Needle  ...............   197 

82.  Control  by  Large-scale  Magnetic  Traverse  with  Plane-table  ____   199 

83.  Traversing  by  Plane-table  with  Deflection  Angles  .............  200 

84.  Intersection  from  Traverse  ....................................  202 

85.  Engineers'  Transit  .............................................  203 

86.  Adjustments  of  the  Transit  ....................................  204 

87.  Traversing  with  Transit  .......................................  207 

88.  Platting  Transit  Notes  with  Protractor  and  Scale  ..............  210 

89.  Protractors    ...................................................  210 

90.  Platting  Transit  Notes  by  Latitudes  and  Departures  ..........  212 

91.  Prismatic  Compass  ............................................  214 

92.  Magnetic  Declination  ..........................................  221 

93.  Secular  Variation  and  Annual   Change  ........................  222 

94.  Local    Attraction  ..............................................  223 

CHAPTER   XI. 

LINEAR   MEASUREMENT   OF   DISTANCES. 

95.  Methods  of  Measuring  Distances;    Pacing  ......................  224 

96.  Distances  by  Time  ............................................  226 

97.  Measuring  Distance  with  Linen  Tape  .........................  228 

98.  Odometer    ....................................................  22Q 

99.  Chaining   .....................................................  234 

CHAPTER    XII. 

STADIA   TACHYMETRY. 

100.  Tachymetry    ...............................  ;  ____  f  _  g 

101.  Topography   with    Stadia  ........................  .......  .'237 

102.  Tachymetry  with  Stadia  .........................  2,g 

103.  Accuracy  and  Speed  of  Stadia  Tachymetry  .......  ....].  .  240 

104.  Stadia  Formula  with  Perpendicular  Sight  ..........  ............  243 

105.  Stadia   Formula  with   Inclined   Sight  ...............  246 


CONTENTS.  XI 

ART.  PAGE 

106.  Determining  Horizontal  Distances  from  Inclined  Stadia  Meas- 

ures      249 

107.  Horizontal  Distances  and  Elevations  from  Stadia  Readings 249 

108.  Determining  Elevations  by  Stadia 258 

109.  Diagram  for  Reducing  Stadia  Measures 259 

1 10.  Diagram  for  Reducing  Inclined  Stadia  Distances  to  Horizontal..  264 
in.  Effects  of  Refraction  on   Stadia   Measurements 266 

112.  Stadia-rods    269 

CHAPTER    XIII. 

ANGULAR   TACHYMETRY. 

113.  Angular  1'achymetry  with  Transit  or  Theodolite 272 

114.  Measuring  Distances  with  Gradienter 274 

115.  Wagner-Fennel  Tachymeter 280 

1 16.  Range-finding   282 

117.  Surveying   with    Range-finder 283 

118.  Traversing  with    Range-finder 284 

1 19.  Weldon  Range-finder 280 

120.  Accuracy  and  Difficulties  of  Range-finding 289 

121.  Range-finding  with  Plane-table 290 

CHAPTER    XIV. 

PHOTOGRAPHIC  SURVEYING. 

122.  Photo-surveying  29:.* 

123.  Photo-surveying  and   Plane-table   Surveying   Compared 292 

124.  Principles   of   Photo-topography 296 

125.  Camera    and    Plates 298 

126.  Field-work  of  a  Photo-topographic  Survey 293 

127.  Projecting  the  Photo-topographic  Map 300 


PART   III. 

HYPSOMETRY,  OR  DETERMINATION  OF  HEIGHTS. 
CHAPTER   XV. 

SPIRIT-LEVELING. 

128.  Hypsometry  305 

129.  Spirit-leveling 306 

130.  Engineering    Spirit-levels 308 


xii  CONTENTS. 

ART.  PAGK 

131.  Adjustments  of  the  Level 308 

132.  Target   Leveling-rods 311 

133.  Speaking-rods    3*3 

134.  Turning-points    3*5 

135.  Bench-marks   3l6 

136.  Method  of  Running  Single  Lines  of  Levels 317 

137.  Instructions  for  Leveling 320 

138.  Note-books 322 

139.  Platting  Profiles 324 

CHAPTER   XVI. 

LEVELING  OF   PRECISION. 

140.  Precise    Leveling 325 

141.  Binocular  Precise   Level 326 

142.  Precise   Spirit-level 327 

143.  Sequence  in  Simultaneous  Double-rodded  Leveling 329 

144.  Methods  of  Running 332 

145.  Precise   Rods 332 

146.  Manipulation  of  Instrument 336 

147.  Length   of   Sight 337 

148.  Sources  of  Error 339 

149.  Divergence  of  Duplicate  Level  Lines 343 

150.  Limit  of  Precision 344 

151.  Adjustment  of  Group  of  Level  Circuits 345 

152.  Refraction  and  Curvature 347 

153.  Speed   in    Leveling 349 

154.  Cost  of  Leveling : 349 

155.  Long-distance   Precise   Leveling 352 

156.  Hand-levels    355 

157.  Using  the  Locke  Hand-level '. . .  356 

158.  Abney   Clinometer   Level 357 

CHAPTER    XVII. 

TRIGONOMETRIC   LEVELING. 

159-  Trigonometric    Leveling 359 

160.  Vertical    Angulation 361 

161.  Vertical  Angulation,  Computation 363 

162.  Vertical  Angulation  in  Sketching 363 

163.  Vertical  Angulation  from  Traverse 367 

164.  Trigonometric  Leveling,   Computation 368 

165.  Errors  in  Vertical  Triangulation 370 

166.  Refraction   and    Curvature 371 

167.  Leveling  with  Gradienter 372 


CONTENTS.  xiii 

CHAPTER   XVIII. 

BAROMETRIC   LEVELING. 

ART.  PAGE 

168.  Barometric  Leveling 374 

169.  Methods  and  Accuracy  of  Barometric  Leveling 375 

170.  Mercurial    Barometer 376 

171.  Barometric  Notes  and  Computation 378 

172.  Example  of  Barometric  Computation 381 

173.  Guyot's    Barometric    Tables 383 

174.  Aneroid   Barometer 395 

175.  Errors  of  Aneroid 395 

176.  Using  the  Aneroid 396 

177.  Thermometric  Leveling 402 


PART   IV. 

OFFICE  WORK  OF  TOPOGRAPHIC  MAPPING. 
CHAPTER   XIX. 

MAP   CONSTRUCTION. 

178.  Cartography 404 

179.  Map    Projection 405 

180.  Kinds    of    Projections 405 

181.  Perspective   Projections 406 

182.  Cylinder  Projections 410 

183.  Conical  Projections 412 

184.  Constructing  a   Polyconic   Projection 416 

185.  Projection  of  Maps  upon  a  Polyconic  Development 418 

186.  Use  of  Projection  Tables 435 

187.  Areas  of  Quadrilaterals  of  Earth's  Surface 436 

188.  Platting  Triangulation  Stations  on  Projection 437 

189.  Scale  Equivalents 446 

CHAPTER   XX. 

TOPOGRAPHIC   DRAWING   AND   RELIEF   MODELING. 

190.  Methods  of  Map  Construction 449 

191.  Topographic   Drawing 449 

192.  Contour    Lines 455 

193.  Contour    Construction 460 


XIV  CONTENTS. 

194.  Hachures   4$i 

195.  Conventional  Signs 463 

196.  Lettering   • 477 

197.  Drafting    Instruments 477 

198.  Model  and  Relief  Maps 478 

199.  Modeling  the  Map 480 

200.  Duplicating  the  Model,  Casting 485 

WORKS  OF  REFERENCE  ON  TOPOGRAPHY 49° 


PART  V. 

TERRESTRIAL  GbODESY. 
CHAPTER   XXI. 

FIELD-WORK   OF  BASE  MEASUREMENT. 

201.  Geodesy 495 

202.  Base   Measurement 497 

203.  Accuracy    of    Base    Measurement 498 

204.  Base  Measurement  with  Steel  Tapes 500 

205.  Steel    Tapes 501 

206.  Tape-stretchers    501 

207.  Laying  out  the  Base 505 

208.  Measuring  the  Base 507 

209.  Compensated    Base    Bars 507 

210.  Contact-slide  Base  Apparatus 508 

211.  Iced-bar  Apparatus 511 

212.  Repsold   Base   Apparatus 514 

213.  Base  Lines:    Cost,  Speed,  and  Accuracy 516 

CHAPTER   XXII. 

COMPUTATION   OF   BASE   MEASUREMENT. 

214.  Reduction  of  Base  Measurement 517 

215.  Reduction  to  Standard 517 

216.  Correction  for  Temperature 518 

217.  Record  of  Base  Measurement 518 

218.  Correction  for  Inclination  of  Base 519 

219.  Correction  for  Sag 521 

220.  Reduction  of  Base  to  Sea-level 522 

221.  Summary  of  Measures  of  Sections '. 523 


CONTENTS.  XV 

ART.  PAGE 

222.  Corrected   Length   of  Base 523 

223.  Transfer  of  Ends  of  Base  to  Triangulation  Signals 524 

224.  Other  Corrections  to  Base  Measurements 526 

225.  To  Reduce  Broken  Base  to  Straight  Line 526 

CHAPTER    XXIII. 

FIELD-WORK   OF    PRIMARY   TRAVERSE. 

226.  Traverse  for  Primary  Control 527 

227.  Errors  in  Primary  Traverse 528 

228.  Instruments  Used  in  Primary  Traverse 529 

229.  Method  of  Running  Primary  Traverse 531 

230.  Record  and  Reduction  of  Primary  Traverse 532 

231.  Instructions  for  Primary  Traverse 533 

232.  Cost,  Speed,  and  Accuracy  of  Primary  Traverse 536 

CHAPTER   XXIV. 

COMPUTATION   OF   PRIMARY  TRAVERSE. 

233.  Computation   of   Primary   Traverse 538 

234.  Correction  for  Observed  Check  Azimuths 539 

235.  Computation   of   Latitudes  and   Longitudes 540 

236.  Corrected   Latitudes   and    Longitudes 542 

CHAPTER   XXV. 

FIELD-WORK   OF    PRIMARY   TRIANGULATION. 

237.  Primary  Triangulation 545 

238.  Reconnaissance  for  Primary  Triangulation 546 

239.  Intervisibility  of  Triangulation  Stations 549 

240.  Accuracy  of  Triangulation 553 

241.  Instruments    553 

242.  Micrometer    Microscope 556 

243.  Triangulation   Signals 5591 

244.  Tripod  and  Quadripod  Signals 561 

245.  Observing  Scaffolds 565 

246.  Heliotrope    566 

247.  Night   Signals 574 

248.  Station-  and  Witness-marks : 575 

CHAPTER    XXVI. 

MEASUREMENT   OF   ANGLES. 

249.  Precautions  in  Measuring  Horizontal  Angles 577 

250.  Observer's  Errors  and  their  Correction 578 


XVI  CONTENTS. 

ART.  PACK 

251..  Instrumental  Errors  and  their  Correction 580 

252.  Methods  of  Measuring  Horizontal  Angles 584 

253.  Record  of  Triangulation  Observations 588 

254.  Instructions  for  Field-work  of  Primary  Triangulation 590 

255.  Primary  Triangulation— Cost,  Speed,  and  Accuracy 592 

CHAPTER   XXVII. 

SOLUTION   OF  TRIANGLES. 

256.  Trigonometric   Functions 594 

257.  Fundamental  Formulas  for  Trigonometric  Functions 594 

258.  Formulas  for  Solution  of  Right-angled  Triangles . ...  594 

259.  Solution  of  Plane  Triangles 596 

260.  Given  Two  Sides  and  Included  Angle,  to  Solve  the  Triangle 598 

261.  Given  Certain  Functions  of  a  Triangle,  to  Find  Remainder 598 

262.  Given  Three  Sides  of  a  Triangle,  to  Find  the  Angles 599 

263.  Three-point  Problem 600 

CHAPTER   XXVIII. 

ADJUSTMENT   OF   PRIMARY  TRIANGULATION. 

264.  Method  of  Least  Squares 602 

265.  Rejection  of  Doubtful   Observations 604 

266.  Probable  Error  of  Arithmetic  Mean 607 

267.  Reduction   to   Center 608 

268.  Station  Adjustment 611 

269.  Routine  of  Station  Adjustment 612 

270.  Equations   of   Condition 612 

271.  Formation  of  Table  of  Correlates 614 

272.  Formation  of  Normal  Equations  and  Substitution  in  Table  of 

Correlates   615 

273.  Figur-e  Adjustment 616 

274.  Routine  of  Figure  Adjustment 617 

275.  Notation  Used  in  Figure  Adjustment 618 

276.  Angle  Equations 619 

277.  Spherical   Excess 619 

278.  Side  Equations .....,.< 623 

279.  Solution  of  Angle  and  Side  Equations 625 

280.  Correlates  and  Normal  Equations 627 

281.  Algebraic  Solution  of  Normal  Equations 628 

282.  Substitution  in  Normal  Equations 632 

283.  Substitution  in  Table  of  Correlates 632 

284.  Weighted  Observations: 633 


CONTENl^S.  XV11 

CHAPTER   XXIX. 

COMPUTATION   OF  DISTANCES  AND   COORDINATES. 

ART.  PACK 

285.  Geodetic  Coordinates 636 

286.  Computation  of  Distances 637 

287.  Formulas  for  Computing  Geodetic  Coordinates 638 

288.  Computation  of  Geodetic  Coordinates:    Example 642 

289.  Knowing  Latitudes  and  Longitudes  of  Two  Points,  to  Compute 

Azimuths  and  Distances 646 

CHAPTER    XXX. 

GEODETIC   CONSTANTS   AND   REDUCTION   TABLES. 

290.  Constants  Depending  on  Spheroidal  Figure  of  Earth 672 

291.  Numerical   Constants 672 

292.  Length  of  the  Meter  in  Inches 674 

293.  Interconversion  of  English  and  Metric  Measures 675 

294.  Logarithms  and  Factors  for  Conversion  of  English  and  Metric 

Measures  676 


PART   VI. 

GEODETIC  ASTRONOMY. 
CHAPTER    XXXI. 

ASTRONOMIC   METHODS. 

295.  Method  of  Treatment  .........................................  678 

296.  Geodetic  Astronomy  ...........................................  679 

297.  Definitions  of  Astronomic  Terms  ..............................  679 

298.  Astronomic  Notation  ..........................................  683 

299.  Fundamental  Astronomic  Formulas  ............................  684 

300.  Finding  the  Stars  .............................................  685 

301.  Parallax    ......................................................  688 

302.  Refraction   .......  .............................................  689 

CHAPTER    XXXII. 


303.  Interconversion  of  Time  .......................................  695 

304.  Interconversion  of  Time  and  Arc  ..............................  698 


Xviii  CONTENTS. 

ART.  *AGK 

305.  Determination  of  Time ?o° 

306.  Time  by  a  Single  Observed  Altitude  of  a  Star 702 

307.  Approximate  Time  from  Sun 703 

308.  Time   by   Meridian   Transits 7°3 

CHAPTER   XXXIII. 

AZIMUTH. 

309.  Determination  of  Azimuth 7°7 

310.  Observing   for   Azimuth 707 

311.  Approximate   Solar   Azimuth 708 

312.  Azimuths  of  Secondary  Accuracy 712 

313.  Primary  Azimuths 7J9 

314.  Reduction   of  Azimuth    Observations 720 

315.  Azimuth  at  Elongation 721 

CHAPTER   XXXIV. 

LATITUDE. 

316.  Methods  of  Determining  Latitude 723 

317.  Approximate  Solar  Latitude 724 

318.  Latitude  from  an  Observed  Altitude 725 

319.  Astronomic  Transit  and  Zenith  Telescope 726 

320.  Latitude  by  Differences  of  Zenith  Distances  of  Two  Stars 728 

321.  Errors  and  Precision  of  Latitude  Determinations 729 

322.  Field-work  of  Observing  Latitude 730 

323.  Determination  of  Level  and  Micrometer  Constants 732 

324.  Corrections  to  Observations  for  Latitude  by  Talcott's  Method. .  738 

325.  Reduction   of   Latitude    Observations 743 

CHAPTER    XXXV. 

LONGITUDE. 

326.  Determination  of  Longitude 744 

327.  Astronomic  Positions:  Cost,  Speed,  and  Accuracy 744 

328.  Longitude  by  Chronometers 745 

329.  Longitude   by    Lunar   Distances 746 

330.  Longitude   by   Chronograph 748 

331.  Observing  for  Time 751 

332.  Reduction  of  Time  Observations 752 

333.  Record  of  Time  Observations 754 

334.  Longitude   Computation 757 

335.  Comparison  of  Time 774 


CONTENTS.  XIX 

CHAPTER   XXXVI. 

SEXTANT  AND   SOLAR  ATTACHMENT. 
ART.  PACK 

336.  Sextant  777 

337.  Adjustment  of  Sextant 778 

338.  Using  the  Sextant  780 

339.  Solar    Attachment 781 

340.  Burt  Solar  Attachment 781 

341.  Adjustment  of  Burt  Solar  Attachment 782 

342.  Smith  Meridian  Attachment 785 

343.  Adjustment  of  Smith  Meridian  Attachment 786 

344.  Determination  of  Azimuth  and  Latitude  with  Solar  Attachment.  789 

345.  Solar  Attachment  to  Telescopic  Alidade 791 

CHAPTER    XXXVII. 

PHOTOGRAPHIC   LONGITUDES. 

346.  Field-work  of  Observing  Photographic  Longitude 793 

347.  The  Camera  and  its  Adjustments 794 

348.  Measurement  of  the  Plate 797 

349.  Computation  of  the  Plate 801 

350.  Sources  of  Error 802 

351.  Precision  of  Resulting  Longitude 806 

REFERENCE   WORKS   ON   GEODESY 809 


PART   VII. 

CAMPING,  EMERGENCY  SURGERY,  PHOTOGRAPHY. 
CHAPTER    XXXVIII. 

CAMP   EQUIPMENT  AND   PROPERTY. 

352.  Attributes  of  a  Skillful  Photographer 811 

353.  Subsistence  and  Transportation  of  Party  in  Field 813 

354.  Selecting  and  Preparing  the  Camp  Ground 814 

355.  Tents   817 

356.  Specifications  for  Army  Wall  Tents 820 

357.  Specifications  for  Army  Wall-tent  Flies 821 

358.  Specifications  for  Army  Wall-tent  Poles 822 

359.  Specifications  for  Army  Shelter  Tents  (Halves) 822 

360.  Specifications  for  Army  Shelter  Tents  (Poles) 824 

361.  Erecting  the  Tent 825 


CONTENTS. 


ART 


PACK 


362.  Tent   Ditching  and   Flooring  ..................................  825 

363.  Camp  Stoves,   Cots,  and  Tables  ...............................  827 

364.  Specifications  for  Army  Sibley  Tent  Stoves  ....................  829 

365.  How  to  ,  Build  Camp-fires  .....................................  830 

366.  Cooking-fire  for  a  Small  Camp  .................................  830 

367.  Camp  Equipment  ..............................................  831 

368.  Provisions    ....................................................  833 

CHAPTER   XXXIX. 

TRANSPORTATION   EQUIPMENT. 

369.  Camp  Transportation:    Wagons  ................................  836 

370.  Pack  Animals  and  Saddles  ....................................  837 

371.  Moore  Pack-saddles  ...........................................  840 

372.  Throwing  the  Diamond  Hitch  .................................  841 

373.  Packmen    .....................................................  847 

374.  Transportation  Repairs  .........................................  848 

375.  Veterinary    Surgery  ............................................  849 

CHAPTER    XL. 

CARE   OF   HEALTH. 

376.  Blankets  and  Clothing  .........................................  850 

377.  Care  of  Health  ...........................................  .  ____  852 

378.  Drinking-water    ...............................................  855 

379.  Medical   Hints  .................................................  856 

380.  Diarrhea  and  Dysentery  .......................................  857 

381.  Drowning  and  Suffocation  .....................................  858 

382.  Serpent-  and  Insect-bites  ......................................  860 

383.  Surgical   Advice  ...............................................  860 

384.  Medicine-chest    ...............................................  861 

CHAPTER   XLI. 

PHOTOGRAPHY. 

385.  Uses  of  Photography  in  Surveying  ............................  864 

386.  Cameras    ......................................................  865 

387.  Lenses  and  their  Accessories  ..................................  867 

388.  Dry  Plates  and  Films  .........................................  869 

389.  Exposures  ....................................................  872 

390.  Developing    ...................................................  875 

391.  Fixing    .......................................................  878 

392.  Printing  and  Toning  ..........................................  ,  880 

393.  Blue  Prints  and  Black  Prints  ..................................  883 


TABLES. 


TABLE  PAGE 

I.  Scale  and  Cost  of  Detailed  Topographic  Maps 67 

II.  Scale,  Cost,  and  Relief  of  Government  Geographic  Maps  75 

III.  Scale  and  Cost  of  Cadastral  Surveys 107 

IV.  Error  in  Horizontal  Angle  due  to  Inclination  of  Plane- 

table   Board 181 

V.  Logarithms  of  Numbers  to  Four  Places 215 

VI.  Logarithms  of  Trigonometric  Functions 217 

VII.  For    Converting    Wheel-revolutions    into    Decimals    of 

a   Mile 233 

VIII.  Reduction   of   Inclined    Stadia    Measures   to   Horizontal 

Distances 249 

IX.  Horizontal  Distances  and  Elevations  from  Stadia  Read- 
ings    250 

X.  Differences  of  Elevation  from  Stadia  Measures , 260 

XI.  Natural  Sines  and  Cosines '.''.'. 275 

XII.  Natural  Tangents  and  Cotangents 277 

XIII.  Cost  of  Leveling  per  Mile  in  Various  States 350 

XIV.  Cost  and  Speed  of  Government  Precise  Leveling. 351 

XV.  Differences  of  Altitude  from  Angles  of  Elevation  or  De- 
pression   364 

XVI.  Logarithms  of  Radius  of  Curvature  R  in  Meters 369 

XVII.  Reduction  of  Barometric  Readings  to  Feet 384 

XVIII.  Correction  for  Differences  of  Temperature 392 

XIX.  Correction  for  Differences  of  Gravity  at  Various  Latitudes  393 

XX.  Correction  for  Decrease  of  Gravity  on  a  Vertical.  . . . 394 

XXI.  Correction  for  the  Height  of  the  Lower  Station.    Positive  394 
XXII.  Altitude  by  Boiling-point  of  Water 403 

XXIII.  Coordinates  for  Projection  of  Maps 419 

XXIV.  Lengths  of  Degrees  of  Meridian  and  Parallel 437 

XXV.  Arcs  of  the  Parallel 438 

XXVI.  Meridional  Arcs.     Coordinates  of  Curvature 139 

xxi 


XXli  TABLES. 

TABLE  PAG* 

XXVII.  Areas  of  Quadrilaterals  of  Earth's  Surface 445 

XXVIII.  Scale  Equivalents  for  Various  Ratios 447 

XXIX.  Ratios  Equivalent  to  Inches  to  One  Mile 448 

XXX.  Convergence  of  Meridians 54° 

XXXI.  Difference   in   Height  between  the  Apparent  and  True 

Level    549 

XXXII.  Sizes  of  Heliotrope  Mirrors 569 

XXXIII.  Solution  of  Oblique  Plane  Triangles 597 

XXXIV.  Pierce's   Criterion 606 

XXXV.  Factors  for  Computing  Probable  Error 608 

XXXVI.  Log  m  for  Determining  Spherical  Excess 622 

XXXVII.  Factors  for  Computation  of  Geodetic  Latitudes,  Longi- 
tudes, and  Azimuths 649 

XXXVIII.  Corrections  to  Longitude  for  Difference  in  Arc  and  Sine  670 

XXXIX.  Values  of  Log      *        •. 671 

cos  l/2d 

XL.  Log  F 671 

XLI.  Interconversion  of  English  Linear  Measures 673 

XLII.  Interconversion  of  English  Square  Measures , 674 

XLIII.  To  Convert  Metric  to  English  Measures 675 

XLIV.  To  Convert  English  to  Metric  Measures 675 

XLV.  To  Convert  Meters  into  Statute  and  Nautical  Miles 676 

XLVI.  Logarithmic  Constants  for  Interconversion  of  Metric  and 

Common  Measures 676 

XLVII.  Metric    to    Common    System,    with    Factors    and    Log- 
arithms     677 

XLVIII.  Miscellaneous  Metric  Equivalents 677 

XLIX.  Parallax  of  Sun  (/>)  for  First  Day  of  Each  Month 691 

L.  Mean  Refraction  (Rm) 692 

LI.  Correction  (Cb)  to  Mean  Refraction 693 

LIT.  Correction  (Cd)  to  Mean  Refraction 604 

LIII.  Correction  (Co)  to  Mean  Refraction 695 

LIV.  Conversion  of  Mean  Time  into  Sidereal  Time 696 

LV.  Conversion  of  Sidereal  Time  into  Mean  Time 697 

LVI.  Constants  for  the  Interconversion  of  Time  and  Arc 698 

LVII.  Conversion  of  Time  into  Arc 699 

LVIII.  Conversion  of  Time  into  Arc  (continued) 700 

LIX.  Conversion  of  Arc  into  Time 701 

LX.  Approximate  Local  Mean  Astronomic  Times  of  the  Cul- 
minations and  Elongations  of  Polaris  for  the  Year 

1900 7I5 

LXI.  Intermediate  Times  for  Above 716 

LXII.  Azimuths  of  Polaris  at  Elongation 717 

LXIII.  Corrections  to  Azimuths  of  Polaris  for  Each   Month...  717 


TABLES. 


TABLE  PAGE 

LXIV.  Azimuths  of  Polaris 718 

LXVI.  Values  of  m  for  Every  5°  Declination 737 

LXVII.  Reduction  of  Observations  on  Close  Circumpolar  Stars..  738 

LXVIII.  Correction  for  Differential  Refraction 739 

2  sin2  "i/zT 
LXIX.  Values  of — —^- 740 

sin  i 

LXX.  Factors  for  Reduction  of  Transit  Observations 758 

LXXI.  Ration   List 834 

LXXIL  Relative   Times   of   Exposure   for   Different   Stops   and 

Subjects 874 


LIST  OF  ILLUSTRATIONS. 


PLATES  PACK 

I.  Surveying  Under  Difficulties Frontispiece 

II.  Contour  Survey  of  Site  for  Dam,  Snake  River,  Idaho 58 

III.  Sand  Hills,  Bench,  Creek,  etc.,  above  Albany,  N.  Y 136 

IV.  Isogonic  Chart  of  United  States  for  1900 224 

FIGURE 

1.  Diagram  of  Plane-table  Triangulation,  Frostburg,  Md 25 

2.  Roads,  Houses,  and  Locations  Resulting  from  Traverse,  Frost- 

burg,   Md 26 

3.  Adjusted  Sketch  Sheet,   Frostburg,  Md 27 

4.  Completed  Topographic  Map,  Frostburg,  Md 31 

5.  Land  Survey  Control  for  Topographic  Sketching,  North  Dakota  38 

6.  Topographic  Map  on  Land  Survey  Control,  Fargo,  N.  D 41 

7.  Optical  Illusion  as  to  Relative  Heights  of  Divides 45 

8.  Contour  Topographic  Survey  for  Location  of  Mexican  Central 

Railway 50 

9.  Detailed  Contour  Survey  for  Canal  Location 54 

10.  Preliminary  Map  of  Canal,  Montana 56 

11.  Contour  Survey  of  a  Reservoir  Site,  Montana 59 

12.  Portion  of  Jerome  Park  Reservoir  Survey,  New  York 60 

13.  Plan  and  Profile  of  Twin  Lakes  Dam  Site,  Colorado 61 

14.  Topographic  and  Cadastral  Map  of  Baltimore,  Md 66 

15.  Field-sketch  Map  Made  on  Plane-table  in  Alaska 71 

16.  Geographic  Contour  Map  made  from  Fig.  15 72 

17.  Captain  Zebulon  Pike's  Map  about  Pike's  Peak,  Colo.,  1807 78 

18.  Captain  J.  C.  Fremont's  Map  about  Pike's  Peak,  1845 79 

19.  Wheeler  Map  about  Pike's  Peak,  Colo.,  1876 80 

20.  Hayden  Map  about  Pike's  Peak,  Colo.,  1875 81 

21.  U.  S.  Geological  Survey  Sheet  about  Pike's  Peak,  Colo.,  1892..  83 

22.  U.  S.  Geological  Survey  Map  about  Cripple  Creek,  near  Pike's 

Peak,   1894 85 

XXV 


LIST  OF  ILLUSTRATIONS. 


23.  Field  Plane-table  Sheet,  Exploratory  Route  Survey,  Alaska....  88 

24.  Exploratory  Route  Survey,  Alaska.     Final  Drawing 89 

25.  Exploratory  Survey,  Seriland,  Sonora,  Mexico 9° 

26.  Skeleton  of  Route  from  Best  Available  Map 94 

27.  Sketch  Route  of  Fig.  26,  Filled  in  with  Field  Notes 96 

28.  Sketch  Route  of  Fig.  26,  Filled  out  from  Field  Notes  of  Fig.  27. .  97 

29.  Reconnaissance  on  Nile  River  from  Gordon's  Steamer 98 

30.  Reconnaissance  Sketch  of  Arab  Position  at  Abu  Klea 99 

31.  Military  Map  of  Operations  about  South  Mountain 101 

32.  Military  Siege  Map 102 

33.  Cadastral  Map  of  U.  S.  Public  Land  Survey,  Indian  Territory..  106 

34.  Canyon  in  Homogeneous  Rock,  Yosemite  Park,  Cal 115 

35.  Watergaps  and  Pirating  Streams,  Pottsville,  Pa 117 

36.  Erosion  in  Soft  Rock 120 

37.  Erosion  in  Hard  Rock 120 

38.  Erosion  in  Horizontal  Beds  of  Hard  and  Soft  Rock 120 

39.  Erosion  in  Alternate  Beds  of  Soft  and  Hard  Rock 120 

40.  Erosion  in  Soft  Rock  Underlain  by  Hard 120 

41.  Volcanic  Mountain,  Mt.  Shasta,  Cal 123 

42.  Alluvial  Ridge  and  Flood  Plain,  Lower  Mississippi  River 125 

43.  Sand  Dunes,  Coos  Bay,  Ore 127 

44.  Dissected  Plateau,  Northern  Arizona 129 

45.  Mountain  Range  and  Amphitheater,  Irwin,  Col.o 131 

46.  Drawing  Radial  Sight  Lines 148 

47.  Intersecting  on  Radial  Lines 149 

48.  Coast  Survey  Plane-table 154 

49.  Telescopic  Alidade  and  Johnson  Plane-table 155 

50.  Johnson  Plane-table  Movement 156 

51.  Telescopic  Alidade 158 

52.  Gannett  Traverse  Plane-table  and  Sight  Alidade 160 

53.  Vertical  Angle  Sight  Alidade 161 

54.  Folding  Exploratory  Plane-table  and  Small  Theodolite 163 

55.  Cavalry  Sketchboard  and  Straight-edge 165 

56.  Scales  of  the  Slide  Rule 169 

57.  Double  Screw  to  Hold  Plane-table  Paper 177 

58.  Intersections  with  Plane-table 183 

59.  Three-point  Locations 186 

60.  Bessel's  Graphic  Solution  of  Three-point  Problem 189 

61.  Ranging-in   I92 

62.  Lining-in  I93 

63.  Two-point  Problem 194 

64.  Traversing  with  Plane-table 198 

65.  Section  of  Engineers'  Transit 203 

66.  Collimation  Adjustment 206 

67.  Traversing  with  .Transit .208 


LIST  OF  ILLUSTRATIONS.  XXV'ii 

FIGURE  PAGE 

68.  Plat  of  Transit  Road  Traverse 210 

69.  Full-circle  Vernier  Protractor 211 

70.  Three-arm  Protractor 211 

71.  Signs  of  Latitudes  and  Departures 213 

72.  Prismatic   Compass 214 

73.  Douglas  Odometer  Attached  to  Wheel 230 

74.  Bell  Odometer 231 

75.  Hand   Recorder 232 

76.  Stadia  Measurement  on  Horizontal 244 

77.  Stadia  Measurement  on  Slope 248 

78.  Stadia  Reduction  Diagram 259 

79.  Stadia  Reduction  Diagram  to  Horizontal  Distances 265 

80.  Diagram  for  Reducing  Inclined  Stadia  Distances  to  Horizontal..  266 

81.  Speaking  Stadia  and  Level-rods 270 

82.  Angular  Tachymetry 273 

83.  Wagner- Fennel  Theodolite  Tachymeter 281 

84.  Reconnaissance    Sketch-map    with    Cavalry-board    and    Range- 

finder  285 

85.  Range-finding  with  a  Direction-point,  D 287 

86.  Range-finding  without  Direction-point 287 

87.  Measuring  Long  Base  with  Range-finder 287 

88.  Weldon  Range-finder 288 

89.  Range-finding  with   Plane-table 290 

90.  Photograph    by     Canadian    Survey    and    used    in    Map    Con- 

struction   293 

91.  Bridges-Lee  Photo-theodolite 297 

92.  Projection  of  Camera-plates  from  a  Station 301 

93.  Projection  of  Photograph 302 

94.  Construction  of  Map  from  Four  Photographic  Stations 303 

95.  Engineer's  Wye   Level 309 

96.  Target-rods  312 

97.  Speaking    Level-rods 314 

98.  Turning-points    315 

99.  Illustrated  Description  of  Bench-mark 316 

100.  Bronze  Tablet  and  Wrought-iron  Bench-mark  Post...    318 

looa.   New  Coast  Survey   Binocular   Precise  Level 326 

looft.  Section    of  Binocular  Precise  Level  327 

101.  Precise  Spirit-level 328 

102.  Duplicate  Direct  and  Reverse  Leveling  with  Single  Rods 330 

103.  Duplicate  Direct  and  Reverse  Leveling  with  Double  Rod 331 

104.  Single-rodding  with  Two  Rodmen 332 

105.  Duplicate  Rodding,  Both  Lines  Direct  Only 332 

106.  U.  S.  Geological  Survey  Double-target  Level-rod 334 

107.  U.  S.  Geological  Survey  Precise  Speaking-rod 336 

108.  Level  Circuit 346 

109.  Group  of  Connected  Level  Circuits 347 


XXV111  LIST  OF  ILLUSTRATIONS. 

FIGURE  PAGK 

no.  Long-distance  Leveling  Across  Tennessee  River 354 

in.  Locke   Hand-level 356 

112.  Abney  Clinometer  Hand-level 357 

113.  Section  Through  Cistern  and  Tube  of  Mercurial  Barometer....  376 

1 14.  Aneroid  Barometer 398 

115.  Gnomonic  and  Orthographic  Projections 407 

116.  Stereographic  and  External  Projections 408 

117.  Orthographic  Equatorial  Projection 408 

118.  Orthographic  Horizontal  Projection 408 

119.  Stereographic  Equatorial  Projection 409 

1 20.  Stereographic  Meridional  Projection 409 

121.  Stereographic  Horizontal  Projection 409 

122.  Lambert's  Surface-true  Central  Projection 409 

123.  Cylinder  Projections 411 

1 24.  Equidistant  Flat  Projection 41  r 

125.  Mercator's  Cylinder  Projection 411 

126.  Van   der  Grinten's  Circular  Projection 4I2 

127.  Babinet's  Homalographic  Projection  of  the  Whole  Sphere 413 

128.  Tangent  Cone  Projection 414 

129.  Intersecting  Cone  Projection 414 

130.  Equal-spaced  Conical  Projection 415 

131.  Mercator's  Conical  Projection 415 

132.  Equivalent  Conical  Projection 415 

133.  Bonne's  Projection 416 

134.  Construction  of  Polyconic  Projection 417 

135.  Contour  (£>),  Shade-line  (B),  and  Hachure  Construction  (A)...  451 

136.  Shaded  Contour  Map 453 

137.  Sketch  Contours.     Xalapa,  Mexico 455 

138.  Relief  by  Crayon-shading 457 

139.  Contour  Sketch 459 

140.  Contour  Projection , 461 

141.  Hachure   Construction 462 

142.  Shaded   Hachures 463 

143.  Hachured  and  Contoured  Hill  on  Different  Scales 465 

144.  Conventional  Signs;    Public  and  Private  Culture 467 

145.  Conventional  Signs;    Miscellaneous  Symbols  and  Boundary  Lines  469 

146.  Conventional  Signs ;    Hydrography 471 

147.  Conventional  Signs ;    Relief  or  Hypsography 473 

148.  Conventional  Signs;    Lettering 475 

149-  Pantograph  4?8 

150.  Relief  Map  from  Catskill  Model 481 

151.  Relief  Map  from  Contour  Model 4^7 

152.  Coast  Survey  Tape-stretcher 502 

153.  Tape-stretcher  for  Use  on  Railroads 504 

154.  Simple  Tape-stretcher ^os 

155-  Contact-slide  Base  Apparatus 509 


LIST  OF  ILLUSTRATIONS.  XXIX 


156.  Eimbeck  Duplex  Base  Apparatus 512 

157.  Cross-section  of  Iced-bar  Apparatus 514 

158.  Repsold  Base  Apparatus 515 

159.  Transfer    of    Measured    Base    OO'    to    Computed    and    Marked 

Base  AB 525 

160.  Intervisibility  of  Objects 551 

161.  Base   Expansion 555 

162.  Eight-inch  Direction  Theodolite 557 

163.  Section  of  Micrometer  through  Screw  Showing  Comb  and  Cross- 

hairs in  Central  Plan 558 

164.  Quadripod  Signal 563 

165.  Observing  Scaffold  and  Signal 567 

166.  Telescopic  Heliotrope 570 

167.  Steinheil   Heliotrope 572 

168.  Trigonometric    Functions 594 

169.  Graphic   Statement  of   Formulas  for   Solution   of  Right-angled 

Triangles 595 

170.  Solution  of  Triangle  Given  Two  Sides  and  Included  Angle 598 

171.  Solution  of  Triangle  Given  Certain  Functions 598 

172.  Solution  of  Triangle  Given  Three  Sides 599 

173.  Three-point  Problem 600 

174.  Reduction  to  Center 609 

175.  Station  Adjustment 613 

176.  Angle  and  Side  Notation 618 

177.  Angle  and  Side  Equations 624 

178.  Computation  of  Azimuths 642 

179.  Latitude,  Declination,  and  Altitude 683 

1 80.  Conversion  of  Time 698 

i8oa.  Aspects  of  Polaris 713 

181.  Astronomic  Transit  and  Zenith  Telescope 727 

182.  Chronograph    750 

183.  Sextant  778 

184.  Graphic  Illustration  of  the  Solar  Attachment 783 

185.  Smith  Meridian  Attachment 786 

186.  Where  a  Pack-mule  Can  Go '. 813 

187.  A  Pretty  Camp  Ground,  North  Carolina 815 

188.  Wall-tent  with  Fly 818 

189.  Ridge  and  Pole  for  Wall-tent 822 

190.  Shelter  Tents 823 

191.  Jointed  Shelter-tent  Poles 824 

192.  Sod-cloth  and  Ditch 826 

193.  Tent  Stove  and  Pipe 827 

194.  Folding  Camp  Table 829 

195.  Folding  Tin  Reflecting  Baker 832 

1 06.  Camp    Wagon 837 

197.  Full-rigged  Moore  Army  Pack-saddle 840 


XXX  LIST  OF  ILLUSTRATIONS. 

FIGURE  PAGE 

198.  Pack-saddle  Cinches 840 

199.  Lashing  Pack  with  Diamond  Hitch 842 

200.  Loading  Pack-mule  with  Mess-boxes 843 

201.  Packing  on  Men's  Backs,  Adirondacks 846 

202.  Pack-basket    847 

203.  Plane-table  Station  on  Mountain  in  Alaska 851 

204.  Inducing  Artificial  Respiration 859 

205.  Diagram  Showing  Relative  Exposures  at  Different  Times  of  Day 

and  Year 873 


PART   I. 

TOPOGRAPHIC,  GEOGRAPHIC,   AND  EXPLORATORY 
SURVEYING. 


CHAPTER  I. 
KINDS  OF  MAP  SURVEYS. 

I.  Classes  of  Surveys — Surveys  may  be  grouped  under 
three  general  heads : 

1.  Those  made  for  general  purposes,  or  information  sur- 
veys. 

2.  Those  made  for  jurisdictional  purposes,    or  cadastral 
surveys. 

3.  Those  made  for  construction  purposes,  or  engineering 
surveys. 

Information  surveys  may  be  exploratory,  geodetic,  geo- 
graphic, topographic,  geologic,  military,  agricultural,  mag- 
netic, or  hydrographic.  Geodetic  surveys  are  executed  for  the 
purpose  of  determining  the  form  and  size  of  the  earth. 
They  do  not  necessarily  cover  the  entire  surface  of  the 
country,  but  only  connect  points  distant  from  each  other 
20  to  100  miles.  Topographic  and  geographic  surveys  are 
made  for  military,  industrial,  and  scientific  purposes.  To 
be  of  value  they  must  be  based  upon  trigonometric  or  tri- 
angulation  surveys,  but  not  necessarily  of  geodetic  accuracy. 

The  mother  map,  or  that  from  which  all  others  are  derived, 
is  the  topographic  map.  This  is  made  from  nature  in  the  field 


2  KINDS  OF  MAP   SURVEYS. 

by  measures  and  sketches  on  the  ground.  It  is  the  original  or 
base  map  from  which  can  be  constructed  any  variety  of  maps 
for  the  serving  of  separate  purposes.  The  historian  may 
desire  to  make  a  map  which  will  indicate  the  places  upon 
which  were  fought  great  battles,  or  on  which  are  located  the 
ancestral  estates  of  historic  families.  The  geologist  may 
desire  to  indicate  the  location  of  certain  rock  formations. 
The  promoter  of  railways  or  other  engineering  works  may 
desire  to  represent  the  route  of  his  projected  road  or  the 
location  of  city  water-supplies  or  real-estate  subdivisions.  For 
these  several  purposes  the  topographic  or  base  map  furnishes 
the  original  data,  or  foundation,  on  which  can  be  indicated,  in 
colors  or  otherwise,  any  special  class  of  information. 

Cadastral  surveys  define  political  and  private  property 
boundaries  and  determine  the  enclosed  areas.  Such  surveys 
are  executed  for  fiscal  and  for  proprietary  purposes,  and  their 
value  depends  upon  the  degree  of  accuracy  with  which  they 
are  made.  A  cadastral  survey  is  not  necessarily  based  upon 
triangulation  and  may  be  only  crudely  executed  with  com- 
pass and  chain.  To  thoroughly  serve  its  purpose,  however, 
it  should  be  based  on  geodetic  work  of  the  greatest  refine- 
ment. It  does  not  necessarily  cover  the  entire  area  en- 
closed, but  only  points  and  lines  which  mark  the  boundaries. 

Engineering  surveys  are  executed  in  greater  detail  than 
any  of  the  above.  They  may  preferably  follow  some  of 
them  and  are  preliminary  to  the  construction  of  engineer- 
ing works.  They  are  conducted  with  such  detail  as  to  per- 
mit the  computing  of  quantities  of  materials  to  be  moved 
and  the  exact  location  of  the  various  elements  of  the  works 
which  are  to  be  constructed.  Engineering  surveys  may  be 
made  for  the  construction  and  improvement  of  military 
works,  as  forts,  navy  yards,  etc. ;  for  constructing  routes  of 
communication,  as  roads,  electric  lines,  canals ;  for  reclama- 
tion of  land,  as  irrigation  and  swamp  surveys;  for  the  im- 
provement of  natural  waterways,  as  river  and  harbor  sur- 


INFORMATION  SURVEYS.  3 

veys ;  or  for  the  improvement  of  cities,  as  city  water-supply 
and  sewage  disposal. 

2.  Information  Surveys. —  All  surveys  have  a  twofold 
purpose : 

1.  To  acquire  certain  information  relative  to  the  earth; 
and 

2.  To  spread  this  among  the  people. 

The  acquirement  of  the  information  is  the  field  survey. 
The  dissemination  may  be  in  the  form  of  manuscript,  illustra- 
tions, or  sketch  maps,  as  in  the  case  of  exploratory  surveys; 
of  a  map  only,  as  in  the  case  of  topographic  survey  when 
the  map  embodies  the  whole  result ;  or  it  may  be  a  combina- 
tion of  the  two,  as  in  the  case  of  geographic  surveys. 

In  addition  to  the  above  primary  classes  of  information 
surveys  are  the  numerous  minor  differences  in  the  method  of 
field-work,  including  the  instruments  used,  the  degree  of  care 
in  obtaining  the  information,  and  the  mode  of  recording  the 
results  in  notes  or  maps.  The  instrumental  work  of  explora- 
tory surveys  is  usually  of  the  crudest  and  most  haphazard 
kind,  the  observations  having  to  be  taken  and  the  notes  re- 
corded incidentally  and  by  such  means  and  at  such  time  as 
the  primary  necessities  of  the  expedition,  those  of  moving 
forward  over  the  route  traversed,  will  permit.  Moreover, 
from  the  necessity  of  the  circumstances  such  surveys  are 
rarely  homogeneous,  never  covering  completely  any  given 
area;  else  they  would  cease  to  be  exploratory.  Being  dis- 
connected, they  are  fixed  from  time  to  time  with  relation  to 
the  earth  by  such  astronomic  observations  as  will  fre- 
quently check  the  interrupted  route  surveys  in  relation  one 
to  the  other. 

Topographic-  and  geographic  surveys  differ  essentially 
from  exploratory  surveys,  but  from  each  other  only  in  minor 
details  of  scale,  degree  of  representation  of  relief,  and  the 
note  taken  of  the  sphericity  of  the  earth.  Topographic  sur- 
veys are  generally  executed  on  so  large  a  scale  and  with  such 


4  KINDS  OF  MAP  SURVEYS. 

care  and  detail  that  account  need  rarely  be  taken  of  the 
sphericity  of  the  earth  in  plotting  the  resulting  map,  and  they 
are  therefore  based  on  geodetic  data  only  as  they  merge  into 
geographic  surveys.  Moreover,  all  important  natural  and 
artificial  features  may  be  represented  on  the  resulting  map 
because  of  its  large  scale. 

Geographic  surveys  merge  imperceptibly,  on  the  one  hand, 
into  topographic  surveys,  as  the  scale  of  the  latter  becomes 
so  small  and  the  area  depicted  on  a  given  map  sheet  so  large 
that  the  shape  of  the  earth  must  be  considered.  On  the 
other  hand,  they  may  be  plotted  on  so  small  a  scale  and  the 
relief  be  depicted  by  such  approximate  methods  that  they 
merge  imperceptibly  into  exploratory  surveys,  being  practi- 
cally of  the  same  nature  as  the  latter  excepting  that  they 
cover  a  given  area  in  its  entirety. 

3.  Topographic  Surveys.  —  A  topographic  map  is  one 
which  shows  with  practical  accuracy  all  the  drainage,  culture, 
and  relief  features  which  the  scale  of  representation  will  per- 
mit. Such  scale  may  be  so  large  and  the  area  represented 
on  a  given  map  sheet  be  so  small  that  the  control  for  the 
field  surveys  will  be  procured  by  means  of  plane  and  not  of 
geodetic  surveying.  On  the  other  hand,  the  scale  may  be  so 
small  and  the  area  represented  on  the  given  map  sheet  so 
large  as  to  require  control  by  geodetic  methods. 

The  mistake  is  often  made  of  assuming  that  a  topographic 
map  is  special  and  not  general.  It  is  general,  as  it  is  not 
made  for  the  purpose  of  constructing  roads  and  highways, 
though  it  becomes  a  very  valuable  aid  in  their  projection ; 
nor  is  it  made  for  the  purposes  of  reclaiming  swamp-land  or 
irrigating  arid  land,  but  it  furnishes  general  information 
essential  to  a  preliminary  study  and  plan  for  their  improve- 
ment. The  outcome  of  a  topographic  survey  being  a  topo- 
graphic map,  it  should  be  judged  by  the  map,  and  the  map 
should  be  judged  by  the  manner  in  which  it  serves  the  gen- 
eral purpose.  Above  all,  of  two  maps  or  works  of  any  kind 


FEATURES  ON   TOPOGRAPHIC  MAPS.  5 

made  for  the  same  purpose  and  serving  that  purpose  equally 
well,  that  the  cheaper  one  is  the  better  is  a  well-recognized 
principle  of  engineering. 

In  the  prosecution  of  a  general  topographic  survey  only 
such  primary  points  should  be  determined  geodetically  as  are 
essential  to  the  making  of  the  map.  About  one  such  point 
per  one  hundred  square  miles  is  a  fair  average  for  a  one-mile  to 
one-inch  map.  Such  spirit-level  bench-marks  should  be  set 
and  recorded  as  are  obtained  in  carrying  bases  for  levels  over 
the  area  under  survey.  On  the  above  scale  about  one  bench 
to  five  square  miles  is  a  fair  average. 

4.  Features  Shown  on  Topographic  Maps. — The  fea- 
tures exhibited  on  topographic  maps  may  be  conveniently 
grouped  under  the  three  following  heads : 

1.  The  hydrography,  or  water  features,  as  ponds,  streams, 
lakes. 

2.  The  hypsography,  or  relief  of  surface  forms,  as  hills, 
valleys,  plains. 

3.  The  culture,  or  features  constructed  by  man,  as  cities, 
roads,  villages,  and  the  names  printed  upon  the  map. 

In  order  that  these  various  features  may  be  readily  dis- 
tinguishable and  thus  give  legibility  to  the  map,  it  is  usual  to 
represent  the  hydrography  in  blue,  the  relief  in  brown,  and 
the  culture  in  black.  In  addition  to  this,  wooded  areas  may 
be  indicated  in  a  green  tint. 

The  object  of  a  topographic  survey  is  the  production  of  a 
topographic  map.  Hence  the  aim  of  the  survey  should  be  to 
produce  only  the  map ;  neither  time  nor  money  should  be 
wastefully  expended  in  the  erection  or  refined  location  of 
monuments;  the  demarkation  of  public  or  private  boundary 
lines;  or  the  establishment  of  bench-marks  beyond  such  as 
are  incidental  to  the  work  of  obtaining  field  data  from  which  to 
make  the  map.  The  erection,  location,  and  description  of 
boundary  marks  is  the  special  work  of  a  property  or  cadastral 
survey.  The  erection,  description,  and  determination  of 


6  KINDS   OF  MAP   SURVEYS. 

monuments  and  bench-marks  as  primary  reference  points  is 
the  work  of  a  geodetic  survey.  The  determination  of  many 
unmarked  stations  for  map-making  purposes  is  the  work  of  a 
topographic  survey. 

5.  Public  Uses  of  Topographic  Maps. — For  the  purposes 
of  the  Government  or  State  good  topographic  maps  are  in- 
valuable. They  furnish  the  data  from  which  the  congressman 
or  the  legislator  can  intelligently  discover  most  of  the  informa- 
tion bearing  directly  upon  the  problem  in  hand,  and  they  give 
committees  great  assistance  in  their  decisions  as  to  the  need 
of  legislation.  If  a  River  and  Harbor  bill  is  before  Congress, 
or  a  bill  relating  to  State  Canals  before  the  Legislature,  by  an 
inspection  of  such  maps  the  slopes  of  the  country  through 
which  the  canal  is  to  pass  or  in  which  the  improvements  are 
to  be  made  may  be  readily  ascertained.  The  sources  of  water- 
supply  for  a  canal  or  river  may  be  accurately  measured  on 
such  a  map  and  their  relation  to  the  work  in  hand  intelligently 
ascertained. 

If  the  War  Department  of  the  Government  or  the  Adjutant- 
General's  Office  of  the  State  desires  to  locate  an  arsenal,  en- 
campment ground,  or  other  military  work,  or,  above  all,  if  it 
is  to  conduct  active  military  operations  in  the  field,  such  maps 
serve  all  the  preliminary  purposes  of  the  best  military  maps. 
With  the  addition  of  a  very  little  field-work  during  war  times, 
such  as  the  indication  of  ditches,  fence  lines,  outbuildings, 
etc.,  on  the  mother  or  topographic  map,  a  perfect  military 
map  may  be  obtained. 

For  the  Post-office  Department  or  private  stage,  express,  or 
telephone  companies,  such  maps  furnish  the  basis  on  which 
an  accurate  understanding  can  be  had  of  contracts  submitted 
for  star  or  other  routes  for  carrying  the  mails  or  packages. 
As  these  maps  show  the  undulations  of  the  surfaces  over 
which  roads  pass,  their  bends  and  the  relative  differences  in 
length,  the  difficulties  in  travel  on  competing  roads  can  be 
readily  ascertained  from  them. 


PUBLIC    USES  OF   TOPOGRAPHIC  MAPS.  7 

The  Land  Departments  of  the  Government  and  State  can 
discover  on  such  maps  not  only  the  outlines  of  the  property 
under  their  jurisdiction,  but  its  surface  formation.  Forestry 
Boards  can  see  indicated  upon  these  maps  the  outlines  of  the 
various  wooded  areas,  besides  the  slopes  of  the  lands  on  which 
these  woods  are  situated,  their  relation  to  highways  of  trans- 
portation, railways,  or  streams,  and  the  slopes  to  be  encoun- 
tered in  passing  through  the  woods  on  these  highways. 

The  Legal  department  of  the  Government  or  State  finds 
these  maps  of  service  in  discussing  political  or  property  bound- 
ary lines,  in  ascertaining  within  what  political  division  crimes 
are  committed,  or  individuals  reside  with  whom  the  officers  of 
the  law  desire  to  communicate.  It  is  difficult  to  see  how  any 
systematic  or  economical  plan  of  road  improvement  can  be 
advantageously  made  without  the  knowledge  of  existing  grades, 
the  physiography  of  the  district  through  which  the  roads  pass, 
and  the  location  of  quarries,  which  such  maps  present. 

The  whole  system  of  making  successive  special  surveys  or 
maps  for  every  new  need  is  one  of  the  most  wasteful  in  our 
present  public  practice,  nor  can  it  be  otherwise  until  one  survey 
shall  be  made  that  answers  all  important  official  uses.  The 
amount  of  money  that  has  been  expended  in  making  small 
maps  of  numerous  cities  and  villages  would  have  mapped,  on 
a  general  scale,  many  times  the  area  of  the  country.  Even 
when  we  have  these  special  maps  they  do  not  fully  answer  the 
purpose  for  which  they  were  intended,  as  they  only  show  the 
small  area  included  within  the  immediate  plan  of  operations. 
The  value  of  a  stream  for  economic  purposes  cannot  be  fully 
ascertained  by  an  examination  of  the  stream  at  the  point  from 
which  it  is  to  be  used,  but  the  drainage  basin  from  which  it 
derives  its  supply  should  be  surveyed,  and  its  area  and  slopes 
be  known.  A  good  topographic  map  not  only  shows  the  re- 
lations between  the  natural  and  artificial  features  in  the  im- 
mediate neighborhood  under  consideration,  but  it  shows  the 
relations  of  these  to  the  surrounding  country. 


8  KINDS   OF  MAP  SURVEYS. 

6.  Degree  of  Accuracy  Desirable  in  Topographic  Sur- 
veys.  It  is  difficult  to  set  any  standard  for  the  amount  of  de- 
tail which  the  topographer  must  sketch  on  his  map,  or  the 
amount  of  control  which  must  be  obtained  for  the  checking 
of  this  detail.  A  topographic  map  may  be  so  made  as  to  serve 
many  useful  purposes  and  yet  be  almost  wholly  a  sketch, 
scarcely  controlled  by  mathematical  locations.  The  same 
territory  may  be  mapped  on  the  same  scale  with  little  improve- 
ment in  the  quality  of  representation  of  topographic  form  and 
yet  the  work  be  done  with  such  detail  and  accuracy  and  such 
amount  of  control  as  to  make  it  useful  for  all  practical  pur- 
poses to  which  its  scale  adapts  it. 

With  these  facts  clearly  in  view,  it  is  evident  that  explicit 
instructions  to  the  topographer  are  a  practical  necessity.  Un- 
like any  other  surveyor  the  topographer  must  use  his  own 
judgment  or  be  guided  by  instructions  regarding  the  amount 
of  time  and  money  to  be  spent  in  obtaining  detail  and  control, 
since  the  latitude  permissible  in  mapping  the  same  territory 
on  the  same  scale  varies  greatly  according  to  the  uses  to 
which  the  map  is  to  be  put.  Such  instructions  should  in- 
terpret the  significance  of  scale  and  contour  interval,  and 
should  cover  the  technical  details  of  operations  as  found  ap- 
plicable to  conditions  and  locality  (Art.  7).  They  should 
also  fix  the  method  of  making  and  preserving  field-notes. 
There  are  a  variety  of  methods  of  survey,  of  instruments,  and 
of  records  which  are  generally  applicable  to  any  case,  yet  to 
the  expert  topographer  there  is  practically  only  one  best  way 
for  each,  and  this  can  be  decided  only  after  he  has  inspected 
the  country  or  has  otherwise  acquired  knowledge  of  its 
characteristics. 

The  scale  and  mode  of  expressing  relief  (Art.  191)  must 
be  fixed  as  well  as  the  contour  interval,  if  contours  are  em- 
ployed, in  order  that  all  the  data  necessary  for  the  construc- 
tion of  the  map  on  this  scale  may  be  obtained.  The  methods 
and  instruments  should  be  stated  in  order  that  those  best 


ACCURACY  DESIRABLE.  9 

suited  to  the  conditions  may  be  selected  in  the  beginning. 
The  mode  of  record  should  be  fixed  in  order  that  there  may 
be  uniformity  in  the  results  brought  into  the  office,  provided 
there  are  various  topographers  working  on  the  same  area. 
Such  instructions  are  to  the  topographer  what  specifications 
are  to  the  contractor,  yet  they  cannot  quite  carry  the  force 
of  law  because  of  the  unforeseen  exigencies  which  may  arise 
and  which  require  departure  from  fixed  instructions  in  ac- 
cordance with  the  best  judgment  of  the  topographer. 

In  topographic  mapping  it  is  sometimes  desirable  to  make 
hasty  preliminary  or  reconnaissance  maps  of  a  region  in  order 
that  some  information  of  the  area  may  be  immediately  ob- 
tained. Such  maps  are  practically  sketches  covering  an  ex- 
tensive area  and  without  adequate  framework  of  control,  yet 
they  contain  most  of  the  information  required  in  the  early  de- 
velopment of  the  region.  The  error  has  too  frequently  been 
made  of  giving  such  maps  the  ear-marks  of  accuracy  by  rep- 
resenting the  relief  by  numbered  contours.  In  this  they  are 
misleading.  Contours  indicate  precision  and  should  justly  be 
taken  as  accurate  within  the  limits  of  the  map  scale.  As  has 
been  aptly  stated  by  Mr.  J.  L.  Van  Ornum,  "  accuracy  is  ex- 
pected where  exactitude  is  shown,  and  the  conclusion  is  just 
that  inaccuracy  in  representation  is  inexcusable."  Where 
for  any  reason  the  desired  accuracy  cannot  be  attained  for 
lack  of  the  proper  control,  the  resulting  map  is  merely  a 
sketch-map,  and  relief  should  be  indicated  not  by  contours  but 
by  hachures  or  by  sketched  contours ;  that  is,  lines  in  contour 
form,  but  disconnected  and  unnumbered.  Such  sketch-maps 
are  useful  as  representations  of  topographic  form,  but  are 
valueless  as  base-maps  on  which  to  plan  great  public  improve- 
ments,  the  inception  of  which  is  so  closely  connected  with 
topographic  surveys. 

A  topographic  map  well  executed  is,  to  quote  Captain 
George  M.  Wheeler,  "the  indispensable,  all-important  sur- 
vey, being  general  and  not  special  in  character,  which  under- 


10  KINDS   OF  MAP  SURVEYS. 

lies  every  other,  including  also  the  graphic  basis  of  the  eco- 
nomic and  scientific  examination  of  the  country.  This  has 
been  the  main  or  principal  general  survey  in  all  civilized  coun- 
tries. The  results  of  such  a  survey  become  the  mother  source 
or  map  whence  all  other  fiscal  examinations  may  draw  their 
graphic  sustenance."  Such  a  characterization  of  a  topographic 
survey  can  apply  only  to  one  accurately  made  and  on  which 
every  feature  represented  is  as  accurately  shown  as  the  scale  of 
map  warrants. 

In  planning  a  topographic  survey  the  controlling  factor  of 
the  scale  must  always  be  kept  clearly  in  mind,  as  this  is  the  ul- 
timate criterion  which  decides  the  method  of  survey  and  the 
amount  of  time  and  money  to  be  expended  in  its  execution. 
The  underlying  law  of  topographic  mapping  is  that  applied  to 
other  engineering  works,  namely,  no  part  of  the  construction, 
nor  any  part  of  the  survey,  should  be  executed  with  greater 
detail  or  at  greater  expense  than  will  permit  it  to  safely  per- 
form the  duties  for  which  it  is  intended.  Thus,  in  mapping 
an  extended  area,  traverse  methods  alone  for  horizontal  con- 
trol are  insufficient  unless  performed  with  the  greatest  exacti- 
tude. The  primary  triangulation  on  which  such  a  survey  is 
based  should  be  no  more  accurate  than  will  permit  of  plotting 
the  points  with  such  precision  that  they  shall  not  be  in  error 
by  a  hair's  breadth  at  the  extreme  limit  to  which  the  triangu- 
lation is  extended.  The  secondary  triangulation  should  be 
executed  with  only  such  care  as  will  permit  of  plotting  with- 
out perceptible  error  on  the  scale  selected  and  within  the  lim- 
its controlled  by  the  nearest  primary  triangulation  points.  Sim- 
pler methods  of  securing  horizontal  control  may  be  adopted 
for  the  minor  points  within  the  secondary  triangulation,  and 
these  methods,  be  they  by  plane-table  triangulation  (Chap. 
IX)  or  by  traverse  (Chap.  X),  need  be  nothing  better  than 
will  assure  the  plotting  of  the  result  without  perceptible  error 
and  within  distances  controlled  by  the  nearest  secondary  tri- 
angulation points.  Finally,  minor  details  may  be  obtained  by 


AMOUNT  OF  CONTROL   REQUIRED.  II 

the  crudest  methods  of  traverse,  range-finding,  pacing,  or 
sketch-board  (Arts.  Si,  116,  95,  and  61),  providing  that  the 
distances  on  the  map  over  which  such  methods  are  propagated 
shall  be  so  small  as  to  warrant  their  not  being  perceptibly 
in  error  within  the  limits  of  the  controlling  points  ^  the  next 
higher  order. 

As  with  the  horizontal  control  so  with  the  vertical  control, 
no  more  time  should  be  expended  or  precision  attempted 
in  determining  elevations  than  are  necessary  to  obtain  the 
data  essential  to  the  mapping  of  the  relief  accurately  to  the 
scale  limit.  Where  relief  is  to  be  represented  by  contours  of 
a  small  interval  and  on  a  large  scale,  or  where  the  slopes  of 
the  country  are  gently  undulating  or  comparatively  level,  the 
leveling  must  be  of  a  high  order  that  the  contours  may  be  ac- 
curately placed  in  plan.  In  country  having  slopes  as  gentle 
as  5  to  10  feet  to  the  mile,  a  difference  of  a  few  feet  in 
elevation  may  mean  that  distance  in  error  in  the  horizontal 
location  of  the  contour  if  the  elevations  are  not  determined 
with  accuracy.  On  the  other  hand,  in  precipitous  mountain 
country  much  less  care  is  necessary  in  the  quality  of  the  level- 
ing, since  a  large  error  in  vertical  elevation  may  be  represented 
in  plotting  by  the  merest  fraction  in  horizontal  plan.  For  a 
large  contour  interval  in  country  of  moderate  slopes  less  ac- 
curacy is  essential  in  the  determination  of  the  elevation. 
For  contours  of  20  feet  inte'rval  errors  of  elevation  varying 
from  5  to  20  feet  or  more  may  be  made,  depending  upon  the 
steepness  of  the  slope  and  the  consequent  nearness  in  hori- 
zontal plan  of  one  contour  to  the  next.  The  same  ratio 
applies  to  greater  contour  intervals.  Therefore  the  methods 
pursued  in  determining  the  elevations  should  begin  with  a 
careful  framework  of  spirit-leveling  (Art.  129),  and  the 
amount  of  this  should  be  only  so  great  as  to  insure  that  the 
dependent  levels  of  less  accuracy  shall  not  be  so  far  in  error 
as  to  be  appreciable  for  the  scale  and  contour  interval  selected 
and  for  a  given  slope  of  country.  Based  on  these  spirit-levels 


12  KINDS   OF  MAP   SURVEYS. 

rougher  elevations  by  vertical  angulation  with  stadia  (Art. 
102)  or  by  trigonometric  methods  (Art.  1 59)  may  be  employed, 
and  tied  in  between  these  may  be  elevations  by  aneroid  (Art. 
174),  the  latter  being  checked  at  intervals  sufficiently  frequent 
to  assure  that  the  resulting  elevations  shall  not  introduce  ap- 
preciable errors  in  the  location  of  contours. 

The  same  rules  should  apply  to  the  frequency  with  which 
vertical  control  points  are  determined.  These  should  be  so 
close  together  for  the  scale  of  the  map  and  for  the  contour 
interval  selected  that  in  connecting  them  by  eye  in  the 
course  of  the  sketching  no  error  appreciable  on  the  scale 
shall  be  introduced.  Any  map,  the  best  obtainable,  is  but  a 
sketch  controlled  by  locations.  No  one  would  undertake  to 
determine  the  elevation  and  horizontal  plan  of  every  point  on 
a  contour  line.  Control  positions  on  contours  are  only  deter- 
mined with  sufficient  frequency  to  insure  comparative  accu- 
racy in  connecting  them.  Bearing  on  this  same  point  is  the 
fact  that  such  connection  by  sketching  can  undoubtedly  be 
done  with  greater  accuracy  on  the  plane-table  board  with  the 
terrane  in  view  than  from  notes  platted  up  in  office  or  from 
photographs  or  profile  drawings. 

Where  relief  is  to  be  represented  by  hachures  or  broken 
sketch  contours,  precision  in  absolutely  fixing  the  vertical  ele- 
ment is  of  the  least  moment.  It  is  generally  desirable  in 
making  such  maps  to  write  approximate  altitudes  at  promi- 
nent points,  as  stream  junctions,  villages,  or  mountain  sum- 
mits, but  the  chief  desideratum  is  relative  differences  in  eleva- 
tion in  order  that  the  number  of  the  sketched  contours  and 
their  frequency,  or  the  degree  of  density  of  the  hachuring, 
may  give  an  index  to  the  amount  of  relief. 

7.  Instructions  Relative  to  Topographic  Field-work. 
—The  following  instructions  are  those  issued  by  the  Director 
of  the  United  States  Geological  Survey  for  the  guidance  of 
topographers  in  the  field : 

I.  At  least  two  primary  triangulation  points  or  a  primary  control  line 


INSTRUC7^IONS    TO    TOPOGRAPHERS.  13 

1.  All  primary  triangulatipn   points  and  primary  control  lines  should 
be  platted  on  each  atlas  sheet  previous  to  commencing  field-work. 

2.  All  existing  map  material  should  be  diligently  sought  for;    such  of 
this  as  may  be  of  value,  as  public-land  plats,  railroad,  water-supply,  city, 
Coast  Survey,  Army  Engineer,  or  other  public  or  private  material,  should  be 
carefully  compiled.     If  on  field  inspection  this  proves  adequate,  it  should  be 
brought  up  to  date  and  incorporated  in  the  field  sheets. 

3.  On  each  atlas  sheet,  in  addition  to  primary  levels,  such  other  eleva- 
tions should  be  obtained  instrumentally  that  aneroids  when  used  need  never 
be  left  without  a  check  elevation  for  distances  exceeding  z\  to  3  miles.     These 
control  elevations  may  come  from  profiles  of   railroads,  from  spirit-levels 
or  from  vertical  angulation. 

4.  Plane-table   triangulation   must    be  conducted   on   the   large   sheets, 
and  it  is  desired  that  as  fast  as  intersections  are  obtained  by  the  topog- 
rapher the  vertical   heights   of  stations   and   intersected    points   should  be 
computed. 

5.  In  conducting  plane-table  triangulation,  as  many  prominent  features 
as  possible,  including  hilltops,  churches,  and  houses,  should  be  intersected 
in  order  to  furnish  connections  with  the  traverse  work,  while  gaps  or  passes 
and  salients  on  ridges  should  also  have  their  positions  and  elevations  deter- 
mined from  the  plane-table  stations. 

6.  Secondary   topographic  control  must  precede  topographic  sketching 
and  the  filling  in  of  minor  details  of  the  map. 

7.  Field  sheets  must  be  as  few  in  number  and  as  large  as  the  character 
of  the  topography  will  permit,  and  all  main  control  must  be  adjusted  thereon; 
this  to  be  done  before  the  filling  in  of  minor  detailed  sketching  is  commenced. 
These  minor  details  may  be  obtained  by  traverse  on  separate  sheets,  but 
must  at  once  be  transferred  to  and  adjusted  on  main  field  sheets,  so  that  no 
uncompleted  spaces  shall  be  left  on  them  in  the  field. 

8.  The  stage  of  water  in  rivers  to  be  shown  on  the  topographic  maps  is 
to  be  that  which  exists  during  the  greater  portion  of  the  year  and  represents 
the  normal  condition  of  the  stream.     When  any  other  condition  is  represented 
an    explanatory  note    giving    stage    and    date    should  be    inserted   in   the 
legend. 

9.  The  topographer  in  charge  will  be  held  responsible  not  only  for  the 
quality  of  the  topographic  work  but  also  for  the  quality  and  management 
of  the  spirit-leveling  done  under  his  direction,  and  for  the  location  and  mark- 
ing of  the  bench  marks,  each  of  which  he  should  endeavor  to  examine  person- 
ally.    Standard  bench  marks  should  be  indicated  on  field  sheet. 

10.  Only  so  much  of  the  field  sheets  should  be  inked  in  the  field  as  can 
be  done  with  sufficient  care  to  permit  of  their  being  accepted  as  final  draw- 
ings and  of  their  being  directly  photographed  or  photolithographed  (except 
where  land-survey  plats  are  used  as  field  sheets).     Accordingly,  only  such 


14  KINDS  OF  MAP  SURVEYS. 

inks  should  be  used  as  will  photograph  readily — mixed  burnt  sienna  for 
contours,  black  for  culture,  and  mixed  Prussian  blue  for  drainage. 

11.  A  full  record  must  be  made  on  the  title-page  of  each  notebook,  stating 
character  of  work,  locality,  atlas  sheet,  and  date  of  record;    also  name  of 
topographer  and  maker  of  notes. 

12.  Plats,  on   a   large  scale,  should  be   made  or  obtained  of  all  large 
cities,  showing  the  streets  and  houses  in  detail. 

13.  The  determination  and  spelling  of  names  of  streams,  mountain  peaks, 
villages,  and  other  places  of  note  should  receive  particular  attention. 

14.  Plane-table  stations  must  be  numbered  consecutively  with  Roman 
numerals.     If  the  station  has  been  sighted  before  occupation,  the  station 
number  must  be  followed  by  the  number  of  the  sight  to  it.     Sights  or  points 
must  be  numbered  by  Arabic  numerals  consecutively;    and  a  point  once 
numbered  must  always  be  given  the  same  number  whenever  recognized. 
If  the  points  sighted  exceed  one  thousand  in  number,  a  capital  M  shall  be 
written  at  the  head  of  the  number  column  of  the  notebook.     This  rule  must 
be  followed  by  all  members  of  the  topographic  branch. 

15.  The  standard  conventional  signs  must  be  used  on  all  plane-table  and 
traverse  sheets. 

1 6.  The  sheets  must  be  inked  clearly  and  carefully,   with  uniformity 
throughout,  and  in  such  manner  as  to  adapt  them  for  one-third  reduction  to 
publication  scale.     Only  such  ink  should  be  used  as  will  photograph  readily. 
(See  par.  10,  above.)     Culture  should  be  inked  first,  and  standard  conven- 
tional signs  used. 

17.  In  drawing  streams  care  should  be  taken  that  the  lines  shall  not 
become  faint  and  uncertain  near  the  sources  of  the  streams,  and  the  placing 
of  drainage  in  every  little  gully  simply  to  indicate  that  it  may  be  a  water- 
course should  be  avoided.     Use  the  symbol  dash  and  three  dots  for  intermittent 
streams. 

1 8.  In  lettering,  names  parallel  to  the  east  or  west  sides  of  the  sheet  should 
read  from  the  south  side.     Names  of  minor  importance  and  figures  of  eleva- 
tion should  be  placed  close  to  the  object,  on  the  right  and  horizontally.     The 
letters,  figures,  and  cross  pertaining  to  a  bench  mark  should  be  arranged 
with  the  letters  above  and  to  the  left  of  the  cross,  and  the  figures  below  and 
to  the  right. 

19.  The  original  drawing  of  a  topographic  sheet  shall  be  verified  by 
some  competent  person  in  addition  to  the  topographer  who  compiles  it, 
by  comparison  with  field  sheets,  and  such  "proof -reading"  shall  be  recorded 
on  the  appropriate  form. 

8.  Elements  of  a  Topographic  Survey. — From  a  con- 
structive point  of  view  a  map  is  a  sketch  corrected  by  loca- 
tions. The  making  of  locations  is  geometric,  that  of  sketch- 


ELEMENTS    OF  A     TOPOGRAPHIC  SURVEY.  I  5 

ing  is  artistic.  However  numerous  may  be  the  locations  they 
form  no  part  of  the  map  itself,  serving  merely  to  correct  the 
sketch  which  supplies  the  material  of  the  map.  Every  map, 
whatever  its  scale,  is  a  reduction  from  nature  and  conse- 
quently must  be  more  or  less  generalized.  It  is  therefore  im- 
possible that  any  map  can  be  an  accurate,  faithful  picture  of 
the  country  it  represents.  The  smaller  the  scale  the  greater 
the  degree  of  generalization  and  the  farther  must  the  map  de- 
part from  the,  original.  The  larger  the  scale  the  smaller  the 
area  brought  together  on  a  given  map,  and  the  less  it  appeals 
to  the  eye  which  grasps  so  extended  a  view  of  nature.  There 
is,  however,  for  the  purposes  of  making  information  maps,  a 
scale  which  is  best  suited  to  every  class  of  topography,  and 
the  best  result  only  will  be  obtained  by  selecting  the  relation 
of  horizontal  scale  and  contour  interval  which  fits  the  partic- 
ular topography  mapped. 

By  far  the  most  important  work  of  topographic  mapping 
is  the  sketching  (Arts.  13,  15,  17,  and  193),  and  this  should 
be  done  by  the  most  competent  man  in  the  party — presum- 
ably its  chief.  He  should  not  only  sketch  the  topography 
because  of  his  superior  qualifications  for  that  work,  but  also 
because  the  party  chief  is  responsible  for  the  quality  of  all  the 
work,  and  only  in  the  sketching,  which  is  the  last  act  in  map- 
making,  has  he  full  opportunity  for  examining  the  quality  of 
the  control  and  of  the  other  elements  of  the  work  executed 
by  his  subordinates.  The  map-sketcher  is  therefore  the  topog- 
rapher, and  it  is  in  the  matter  of  generalization  or  in  the  se- 
lection of  scale  and  the  amount  of  detail  which  should  be 
shown  for  the  scale  selected  that  the  judgment  of  the  topog- 
rapher is  most  severely  tested.  This  is  the  work  in  which  the 
greatest  degree  of  proficiency  can  only  be  attained  after  years 
of  experience.  The  topographer  must  be  able  to  take  a  broad 
as  well  as  a  detailed  view  of  the  country,  and  to  understand 
the  meaning  of  its  broadest  features  that  he  may  be  able  best 
to  interpret  details  in  the  light  of  those  features  (Chap.  VI). 


1 6  KINDS   OF  MAP   SURVEYS. 

It  is  only  thus  that  he  can  make  correct  generalizations,  and 
thus  that  he   is   enabled   to   decide  which   detail   should  be 
omitted  and  which  preserved  in  order  to  bring  out  the  pre- 
dominant topographic  features  of  the  region  mapped. 
The  correctness  of  the  map  depends  upon: 

(1)  The  accuracy  of  the  locations; 

(2)  Their  number  per  square  inch  of  map; 

(3)  Their  distribution; 

(4)  The  quality  of  the  sketching. 

The  first  three  of  these  elements  defines  the  accuracy  of 
the  map,  and  the  greatest  accuracy  is  not  always  desirable  be- 
cause it  is  not  always  economical.  The  highest  economy  is 
in  the  proper  subordination  of  means  to  ends,  therefore  the 
quality  of  the  work  should  be  only  such  as  to  insure  against 
errors  of  sufficient  magnitude  to  appear  upon  the  scale  of 
publication  (Art.  6).  The  above  being  recognized,  it  is  evi- 
dently poor  economy  to  execute  triangulation  of  geodetic  re- 
finement for  the  control  of  small-scale  maps,  and,  providing 
the  errors  of  triangulation  are  not  such  as  are  cumulative,  the 
maximum  allowable  error  of  location  of  a  point  on  which  no 
further  work  depends  may  be  set  at  .01  of  an  inch  on  the 
scale  of  publication. 

The  second  condition,  the  number  of  locations  for  the 
proper  control  of  the  sketching,  is  not  easily  defined.  It  de- 
pends largely  upon  the  character  of  the  country  and  the  scale 
and  uses  of  the  map.  Any  estimate  of  it  must  be  based  on 
unit  of  mapped  surface  and  not  of  land  area.  For  rolling  or 
mountainous  country  of  uniform  slopes  or  large  features  (Fig. 
4),  from  \\  to  3  locations  and  2  to  5  inches  of  traverse  per 
square  inch  of  map  should,  with  accompanying  elevations,  be 
sufficient.  On  the  other  hand,  in  highly  eroded  or  densely 
wooded  country  (Fig.  34)  as  many  as  3  to  6  locations  and  5  to 
10  inches  of  traverse,  per  inch  of  map  may,  with  accompany- 
ing elevations,  be  necessary  to  properly  control  the  sketching. 
Again,  in  very  level  plains  country  (Fig.  6)  less  than  one  lo- 


ACCUFACY   OF  MAP.  I/ 

cation  and  but  2  to  5  inches  of  traverse,  with  accurate  eleva- 
tions, will  suffice  to  furnish  adequate  control. 

The  same  is  true  of  the  third  element  of  accuracy,  the 
distribution  of  locations.  In  rolling,  hilly  country  of  uniform 
slope  the  control  should  be  obtained  chiefly  at  tops  and  bot- 
toms and  changes  of  slope.  The  same  is  true  of  heavy  moun- 
tains, excepting  that  all  summits  and  gaps  on  ridges  must  be 
fixed,  as  well  as  all  changes  in  side  slopes  and  a  few  positions 
distributed  about  the  valley  bottoms.  In  flat  plains  the  posi- 
tions determined  should  be  locations  on  the  contours  themselves 
and  at  changes  in  their  direction.  In  highly  eroded  regions 
locations  of  all  kinds  should  be  distributed  with  consider- 
able uniformity,  so  as  to  control  every  change  of  feature  or 
slope. 

The  fourth  element,  the  quality  of  the  sketching,  depends 
wholly  upon  the  artistic  and  practical  skill  of  the  topographer 
— in  other  words,  upon  his  possession  of  the  topographic 
sense,  which  may  be  described  as  his  ability  to  see  things  in 
their  proper  relations  and  his  facility  in  transmitting  his  im- 
pressions to  paper.  This  is  by  far  the  most  important  and 
difficult  requirement  to  meet,  and  one  which  takes  a  longer 
apprenticeship  on  the  part  of  the  topographer  than  all  the 
others  combined. 


CHAPTER  II. 
SURVEYING  FOR  SMALL-SCALE  OR  GENERAL  MAPS. 

9.  Methods  of  Topographic  Surveying. — Three  general 
methods  of  making  topographic  surveys  have  usually  been 
employed  in  the  past : 

First,  traversing  or  running  out  of  contours  by  means  of 
transit,  chain  or  stadia,  and  level; 

Second,  cross-sectioning  the  area  under  survey  with  the 
same  instruments;  and 

Third,  triangulation  of  the  territory  under  survey  with 
such  minuteness  as  to  get  a  sufficient  number  of  vertical  and 
horizontal  locations  to  permit  of  connecting  these  in  office  by 
contour  lines. 

All  three  methods  are  slow  and  expensive,  while  the  first 
two  are  unfitted  to  the  survey  of  large  areas,  because  of  the 
inaccuracies  introduced  in  linear  or  traverse  surveys. 

A  fourth  method,  and  that  which  this  book  is  designed  to 
expound,  is  that  always  employed  by  the  United  States  Geo- 
logical Survey  as  well  as  to  a  lesser  degree  by  several  other 
American  and  European  surveys.  It  is  fitted  to  make  topo- 
graphic maps  for  any  purpose,  on  any  scales,  and  of  any 
area.  '  This  consists  of  a  combination  of  trigonometric, 
traverse,  and  hypsometric  surveying  to  supply  the  controlling 
skeleton,  supplemented  by  the  "  sketching  in  "  of  contour 
lines  and  details  by  a  trained  topographer.  In  this  method 
the  contour  lines  are  never  actually  run  out  nor  is  the  country 
actually  cross-sectioned.  Only  sufficient  trigonometric  con- 
trol is  obtained  to  tie  the  whole  together,  the  minor  control 

18 


METHODS   OF   TOPOGRAPHIC  SURVEYING.  IQ 

between  this  being  filled  in :  first,  in  the  most  favorable  tri- 
angulation  country  almost  wholly  by  trigonometric  methods; 
second,  in  less  favorable  triangulation  country  by  traverses 
connecting  the  trigonometric  points. 

There  are  two  general  methods  of  making  a  contour  topo- 
graphic map  which  have  been  aptly  styled  the  "regular" 
and  the  "irregular."  These  might  be  respectively  called 
the  old  and  the  new.  The  old  or  regular  method  includes  the 
surveying  and  leveling  of  a  skeleton  work  of  controlling 
traverse  or  triangulation  and  the  cross-sectioning  of  the  ter- 
rane  into  rectangular  areas,  the  outlines  of  which  are  trav- 
ersed and  leveled.  In  addition  the  leveled  profiles  and  trav- 
erses are  continued  between  this  gridironing  at  places  where 
important  changes  of  slope  occur,  and  finally  the  survey  and 
leveling  of  flying  lines  or  partial  sections  is  extended  from  each 
station.  By  this  method  the  base  of  each  level  section  or  the 
contour  line  or  line  of  equal  elevation  is  determined  by  setting 
the  instrument  in  position  where  this  level  line  intersects  the 
profile,  and  using  the  telescope  as  a  leveling  instrument  with 
its  cross-hairs  fixed  on  a  staff  at  the  height  of  the  optical  axis, 
a  line  is  then  located  by  tracing  successive  positions  of  a 
stadia  rod  or  by  locating  by  intersection  successive  points  on 
the  level  line,  and  a  line  drawn  through  these  points  locates 
the  contour  curve.  In  addition,  parts  of  several  level  sec- 
tions are  plotted  from  one  station  by  intersection  on,  or  location 
of  a  staff,  and  by  the  determination  of  its  height  above  or 
below  the  instrument  by  vertical  angulation.  In  this  mode 
of  topographic  surveying  pegs  are  usually  driven  at  regular 
intervals  and  their  heights  determined  by  spirit-level  and  ver- 
tical angulation. 

The  new  or  irregular  method  of  topographic  surveying 
consists  in  determining  by  trigonometric  methods  the  po- 
sition and  height  of  a  number  of  critical  points  of  the  terrane 
and  connecting  these  by  traverses  and  levels,  not  run  on  a  cross- 
section  or  rectangular  system,  but  irregularly,  so  as  to  give 


2O  SURVEYING   FOR  SMALL-SCALE   MAPS. 

plans  and  profiles  of  the  higher  and  lower  levels  of  the  country, 
as  ridge  summits  or  divides  and  valley  bottoms  or  drainage  lines, 
such  lines  being  run  over  the  most  easily  traversed  routes,  as 
trails  or  roads.  With  the  numerous  positions  and  heights  deter- 
mined by  the  triangulation,  and  on  these  traverses  as  controlling 
elements,  contour  lines  are  sketched  in  by  eye  and  by  the  aid 
of  the  hand-level  on  a  plane-table  with  the  country  in  con- 
stant view.  This  is  the  method  now  generally  employed  by 
expert  topographers,  and  the  work  is  so  conducted  that  the 
development  of  the  map  proceeds  with  the  survey  of  the 
skeleton  and  rarely  necessitates  the  return  to  a  station  when 
once  occupied.  Moreover,  it  calls  for  the  location  of  less 
points  and  the  running  of  fewer  traverses  and  profiles,  and 
these  over  more  easily  traveled  routes,  than  the  former 
method.  It  is  therefore  more  expeditious,  cheaper,  and  the 
resulting  map  is  a  better  representation  of  the  surface,  as  it 
possesses  not  only  the  mathematical  elements  of  instrumental 
location,  which  in  the  old  method  are  arbitrarily  connected  in 
office,  but  also  the  artistic  element  produced  by  connecting 
the  lines  of  equal  elevation  in  the  field,  with  the  country  at 
all  times  immediately  before  the  eye. 

10.  Geological  Survey  Method  of  Topographic  Survey- 
ing.— In  average  country,  favorable  for  triangulation,  com- 
paratively clear  of  timber  and  well  opened  with  roads,  a  skele- 
ton trigonometric  survey  (Chap.  IX)  is  made,  by  which  the 
positions  and  elevations  of  all  summits  are  obtained,  as  well 
as  the  horizontal  positions  of  a  few  points  in  villages  or  at 
road  crossings,  junctions,  etc.  This  constitutes  the  upper 
system  of  control  (Fig.  i).  Below  and  between  this  is  a  net- 
work of  road  traverses  (Chap.  X)  supplemented  by  vertical- 
angulation  (Chap.  XVII)  or  spirit  levels  (Chap.  XV)  for 
elevations,  and  these  follow  the  most  easy  routes  of  travel, 
not  cross-sectioning  the  country  in  the  true  sense,  but  follow- 
ing all  the  lower  lines  or  stream  bottoms,  as  well  as  the 
gradients  pursued  by  roads  (Fig.  2).  Between  these  two 


RATIONAL   METHOD    OF   TOPOGRAPHIC  SURVEYING,    21 

upper  and  lower  sets  of  control  points  there  are  therefore 
many  intermediate  ones  obtained  by  road  traverses,  and  the 
topographer,  by  observation  from  the  various  positions  which 
he  assumes  and  with  the  knowledge  he  possesses  of  topographic 
forms,  sketches  the  direction  of  the  contour  lines.  These  are 
tied  accurately  to  their  positions  by  the  large  amount  of  mathe- 
matical control  already  obtained,  supplemented  by  additional 
traverses  or  vertical  angles  where  such  are  found  wanting. 
(Art.  162.) 

The  instruments  used  are  as  various  as  are  the  methods  of 
survey  employed ;  the  essential  instruments  being  the 
plane-table  and  the  telescopic  alidade  (Chap.  VII),  which 
invariably  replace  the  transit  (Art.  85)  or  compass  (Art.  91), 
so  that  all  surveying  is  accompanied  by  mapping  at  the  same 
time,  and  there  is  no  tedious  and  confusing  plotting  from  field- 
notes  to  be  done  later  in  office.  Nor  are  any  of  the  sa- 
lient features  of  the  topography  of  the  region  lost  through 
neglect  to  run  traverses  or  obtain  positions  or  elevations,  all 
omissions  of  this  kind  being  evident  from  an  inspection  of 
the  map  while  in  process  of  construction.  The  distances  are 
obtained  by  triangulation  with  the  plane-table  (Art.  73)  and 
by  odometer  measurements  (Art.  98),  supplemented  off  the 
roads  by  stadia  measures  (Chap.  XII)  or  in  very  heavily 
wooded  country  by  chaining  (Art.  99)  and  pacing  (Art.  95). 

The  underlying  principles  of  this  method  of  topography 
are,  first,  a  knowledge  of  and  experience  in  various  methods 
of  surveying,  and  a  topographic  instinct  or  ability  to  appreciate 
topographic  forms,  which  is  acquired  only  after  long  practice; 
and,  second,  a  constant  realization  of  the  relation  of  scale  to  the 
amount  of  control  required  and  methods  of  survey  pursued; 
no  more  instrumental  work  being  done  than  is  actually  re- 
quired to  properly  control  the  sketching,  and  no  more  accu- 
rate method  being  employed  than  is  necessary  to  plotting 
within  reasonable  limits  of  error.  Thus,  where  trigonometric 
locations  (Chap.  IX)  are  sufficiently  close  together,  crude 


22  SURVEYING   FOR   SMALL-SCALE   MAPS. 

odometer  traverses  (Art.  98)  or  even  paced  traverses  (Art.  95) 
can  be  run  with  sufficient  accuracy  to  tie  between  these  with 
inappreciable  errors.  Where  trigonometric  locations  are  more 
distantly  situated,  the  spaces  between  them  must  be  cut  up 
by  more  accurate  traverses,  as  those  with  stadia  (Chap.  XII) 
or  chain  (Art.  99),  these  again  being  gridironed  by  less  accu- 
rate odometer  or  paced  traverses.  Again,  a  primary  system 
of  spirit-leveling  (Chap.  XV)  or  accurate  vertical  triangula- 
tion  (Chap.  XVII)  is  employed  only  for  the  larger  skeleton, 
these  elevations  being  connected  by  less  accurate  vertical- 
angle  lines  or  flying  spirit-levels,  and  these  again  by  aneroid 
(Art.  176),  each  method  being  employed  in  turn  so  that  the 
least  elements  of  control  obtained  may  still  be  plotted  well 
within  a  reasonable  limit  of  error  in  horizontal  location  of 
contour  line. 

Finally,  speed  and  economy  are  obtained  by  traveling 
the  roads  and  trails  in  wheeled  vehicles  or  on  horseback,  at  a 
rapid  gait  from  instrument  station  to  instrument  station ;  the 
slower  process  of  walking  being  only  resorted  to  where  roads 
and  trails  are  insufficient  in  number  to  give  adequate  control 
and  view  of  every  feature  mapped. 

ii.  Organization  of  Field  Survey. — The  party  organiza- 
tion and  the  method  of  distributing  the  various  functions  of 
topographic  surveying  among  the  members  of  the  party  must 
necessarily  differ  with  the  scale  of  the  map  and  the  character 
of  the  region  under  survey.  The  work  involved  in  making  a 
topographic  or  geographic  map  may  comprise  four  operations: 

First.  The  location  of  the  map  upon  the  surface  of  the 
earth  by  means  of  astronomic  observations. 

Second.  The  horizontal  location  of  points,  which  is  usually 
of  three  grades  of  accuracy :  primary  triangulation  or  trav- 
erse ;  secondary  triangulation  or  traverse ;  and  tertiary  trav- 
erse and  meander  for  the  location  of  details. 

Third.  The  measurement  of  heights,  which  usually  ac- 
companies the  horizontal  location  and  may  be  similarly  di- 


ORGANIZATION  OF  FIELD    SURVEY.  2$ 

vided  into  three  classes,  dependent  upon  their  degree  of 
accuracy. 

Fourth.   The  sketching  of  the  map. 

If  the  area  under  examination  is  small  or  the  scale  be  of 
topographic  magnitude,  the  first  of  the  foregoing  operations 
may  be  omitted,  when  the  topographic  party  will  have  (i) 
To  determine  the  horizontal  positions  of  points;  (2)  To 
measure  the  heights  of  these  points;  and  (3)  To  sketch  in  the 
map  details  as  controlled  by  the  horizontal  and  vertical  loca- 
tions so  procured. 

Where  map-making  is  executed  for  geographic  or  explora- 
tory purposes  and  on  a  small  scale  in  open  triangulation  coun- 
try, as  that  in  the  arid  regions  of  the  West,  the  skilled  force 
may  consist  of  only  the  topographer  in  charge.  Where  the 
map  scale  is  increased  up  to  topographic  dimensions  or  the 
country  is  hidden  from  view  by  timber  or  because  of  its  lack 
of  relief,  the  topographer  may  be  assisted  by  one  or  more 
aides  whose  functions  will  be  variously  performed  according 
to  the  conditions  of  the  country. 

12.  Surveying  Open  Country — In  making  a  geographic 
map  on  scales  varying,  say,  from  one-half  mile  to  four  miles  to 
the  inch  in  open,  rolling,  or  mountainous  country  suited  to  tri- 
angulation, all  sketching  and  the  execution  of  the  plane-table 
triangulation  (Chap.  IX)  or  other  control  should  be  done  by 
the  topographer  in  charge.  He  may  be  aided  by  one  to  three 
assistants  according  to  the  speed  with  which  he  is  able  to 
work  and  the  difficulties  encountered  by  the  assistants  in 
leveling  (Chap.  XV).  It  is  assumed  that  the  topographer  has 
a  fixed  area  to  map,  and  that  within  this  area  he  is  in  posses- 
sion of  the  geodetic  positions  (Chap.  XXIX)  of  two  or  more 
prominent  points  and  the  altitude  of  at  least  one. 

With  the  positions  of  these  points  platted  on  his  plane- 
table  sheet  (Art.  188)  he  proceeds,  as  outlined  in  Article  54, 
to  make  a  reconnaissance  of  the  area  for  the  erection  of  sig- 
nals and  to  locate  prominent  points  on  summits  and  in  the 


24  SURVEYING  FOR   SMALL-SCALE  MAPS. 

lower  or  drainage  lines  of  the  country  by  plane-table  triangu- 
lation  (Art.  73).  Meantime,  one  assistant  may  be  running 
lines  of  spirit-levels  (Chap.  XV)  for  the  control  of  the  verti- 
cal element,  while  one  or  two  assistants  are  making  odometer 
(Art.  98)  or  stadia  traverses  (Chap.  XII)  of  roads  or  trails  for 
the  control  of  the  sketching  and  the  mapping  in  plan  of  the 
roads  and  streams.  This  preliminary  control  executed,  the 
topographer  adjusts  to  his  triangulation  locations  the  traverses 
run  by  the  assistants  (Art.  Si),  and  writes  upon  them  in 
their  proper  places  the  elevations  determined  by  leveling  or 
or  vertical  angulation  (Chap.  XVII). 

In  Fig.  I  is  shown  a  typical  triangulation  control  sheet, 
the  directions  of  the  sight  lines  being  indicated  so  as  to  show 
the  mode  of  derivation  of  the  various  locations.  The  stations 
anfl  located  intersection  points  are  numbered  in  order  to  show 
the  sequence  in  which  they  were  procured.  The  traversing 
executed  for  the  same  region  is  illustrated  in  Fig.  2,  from 
which  it  will  be  seen  that  merely  the  plans  of  the  roads  with 
their  various  bends,  stream  crossings,  and  the  houses  along 
them  were  mapped.  Hill  summits  and  other  prominent  ob- 
jects to  one  side  or  other  of  the  traversed  route  were  inter- 
sected (Art.  84)  in  order  to  give  additional  locations  and  to 
facilitate  the  adjustment  of  the  traverse  to  the  triangulation. 
The  closure  errors  of  the  various  traversed  circuits  are  shown, 
and  an  inspection  of  these  makes  it  clear  that  in  every  case 
the  errors  in  traverse  work  are  so  small  as  not  to  affect  the 
quality  of  the  control,  because  the  adjustment  of  the  traverses 
by  means  of  points  on  them  which  are  located  by  the  plane- 
table  triangulation  will  distribute  the  errors  in  .the  various 
road  tangents  in  such  manner  as  to  make  them  imperceptibly 
small  on  the  resulting  map.  The  product  of  such  adjustment 
is  shown  on  Fig.  3,  which  is  the  base  on  which  the  topog- 
rapher begins  his  sketching.  On  this  sketch  sheet  are  the 
locations  obtained  by  him  in  the  execution  of  his  plane-table 
triangulation,  the  traverses  as  adjusted  to  this  control,  and 


SURVEYING    OPEN  COUNTRY. 


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FIG.  i.  —  DIAGRAM    OF    PLAN*.- i ABLE     IRIANGLLATION.     FROSTBURG,    MD. 
Scale 


26  SURVEYING   FOR   SMALL-SCALE  MAPS. 


X 


FIG.   2.— ROADS,   HOUSES,  AND   LOCATIONS   RESULTING   FROM    TRAVERSE. 

FROSTBURG,  MD. 

Scale    ^. 


TOPOGRAPHIC  CONTROL. 


.2005  '1 2100 


FIG.  3.— ADJUSTED  SKETCH  SHEET.     FROSTBURG,  MD. 
Scale 


28  SURVEYING   FOR   SMALL-SCALE   MAPS. 

elevations  from  vertical  angulation  or  spirit-leveling  written 
in  their  appropriate  places. 

If  the  work  be  the  making  of  a  topographic  map  on  scales 
larger  than  those  above  described,  and  the  country  be  still  of 
the  same  topographic  character— namely,  open,  with  salient 
summits, — a  system  of  control  similar  to  the  above  must  in  like 
manner  first  be  executed  by  the  development  of  plane-table 
triangulation  and  the  running  of  control,  traverse,  and  level 
lines.  But  the  after- work  of  sketching  the  map  will  be  con- 
ducted in  a  different  manner  than  for  the  smaller  scales, 
because  of  the  greater  detail  required,  the  shorter  distances 
to  be  traveled  by  the  topographer  in  performing  the  work, 
and  his  consequent  nearness  to  the  various  features  which  he 
is  to  map. 

13.  Sketching  Open  Country.  —  Having  the  control 
platted  on  the  sketch  sheet  as  shown  in  Fig.  3,  and  where 
roads  are  sufficiently  abundant  to  cut  up  the  map  with  trav- 
erses so  near  one  to  the  other  that  the  topographer  may  not 
have  to  sketch  more  than  one-half  to  one  inch  to  either  side 
of  his  position,  the  sketching  of  the  topography  proceeds  as 
follows : 

Taking  the  sketch  sheet  on  a  board  in  his  lap,  the  topog- 
rapher for  cheapness  and  convenience,  because  of  the  speed, 
drives  over  every  road.  Where  these  are  not  sufficiently  near 
one  to  the  other  he  walks  in  between  them,  pacing  distance 
(Art.  95),  and  getting  direction  by  sighting  fixed  objects, 
while  he  sketches  the  plan  of  the  contour  lines  (Art.  193)  as 
far  as  he  can  safely  see  them  to  either  side  of  his  path.  This 
operation  is  performed  by  setting  out  from  such  fixed  points 
as  a  road  junction,  a  located  house,  or  a  stream  crossing,  the 
position  of  which  is  platted  on  his  map  and  the  elevation  of 
which  is  known.  Adjusting  the  index  of  his  aneroid  at  the 
known  elevation  (Art.  176),  he  drives  along,  keeping  the 
platted  direction  of  the  road  parallel  to  its  position  on  the 
ground  and  marking  on  the  map  the  positions  at  which  the 


SKETCHING    OPEN   COUNTRY.  2Q 

various  contours  are  crossed  by  his  route.  Thus,  if  his  contour 
Interval  be  twenty  feet,  at  every  change  of  twenty  feet  as  indi- 
cated by  the  barometer  he  stops,  and,  knowing  his  position 
on  the  map  either  by  reference  to  bends  in  the  roads,  houses, 
or  by  having  counted  the  revolutions  of  his  wheel  from  a 
known  point,  he  glances  along  the  trend  of  the  slopes  to  one 
side  or  the  other,  following  by  eye  the  level  line  of  his  con- 
tour, and  this  he  sketches  in  horizontal  plan  upon  the  map. 
At  first  he  may  be  aided  in  this  by  a  hand-level  (Art.  156), 
but  as  he  acquires  skill  with  practice  he  is  able  to  estimate 
the  position  and  direction  of  the  contour  line  to  either  side 
with  great  accuracy,  and  finally  to  interpolate  other  contours 
above  and  below  that  on  which  he  is  placed  with  such  preci- 
sion as  not  to  affect  the  quality  of  the  resulting  map  by  a  con- 
tour interval. 

The  aneroid  being  an  unreliable  instrument,  he  must  not 
drive  more  than  two  or  three  miles  without  checking  it  at  a 
well-determined  elevation.  This  he  is  usually  able  to  do  at 
houses,  or  hill-summits,  or  other  points  the  positions  of  which 
have  been  determined  by  his  prior  control.  If  he  is  not  able 
so  to  check  his  aneroid,  he  hastily  sets  up  his  plane-table, 
reads  with  the  telescopic  alidade  a  few  vertical  angles  (Art. 
162)  to  hilltops  or  houses  in  sight  and  the  elevations  of  which 
are  known,  and,  with  these  angles  and  the  distances  which  he 
can  measure  from  his  position  to  the  points  sighted  as  shown 
on  the  adjusted  control,  he  is  at  once  able  to  compute  the 
elevation  of  his  position  (Art.  161)  within  two  or  three  feet 
and  thus  check  his  aneroid.  At  the  same  time  he  is  in  simi- 
lar manner  able  frequently  to  throw  out  other  elevations  by 
sighting  from  the  position  thus  determined  to  houses  or  sum- 
mits near  by  which  may  have  been  located  by  the  traverse 
(Art.  84),  and  the  heights  of  which  he  determines  now  from 
his  angulation.  The  topographer  thus  sketches  the  whole 
area  assigned  him,  not  only  mapping  the  contours,  drainage, 
political  boundaries,  and  other  topographic  features,  but  also 


30  SURVEYING   FOR   SMALL-SCALE  MAPS. 

checking  the  positions  of  houses  and  summits  and  the  direc- 
tions and  bends  of  roads  and  streams  as  located  by  the  trav- 
erseman  (Fig.  4). 

Where  the  hills  are  more  prominent  and  the  slopes  bolder 
and  steeper,  the  topqgrapher  sketches  these  from  his  various 
view  points  by  interpolating  contours  between  the  located  con- 
trol points.  With  the  sketch-board  in  his  lap  or  on  the  tripod 
and  approximately  oriented,  looking  about  in  various  direc- 
tions at  hill-summits,  houses  on  slopes,  spurs,  etc.,  which 
may  with  their  elevations  be  platted  on  his  map,  he  first 
sketches  in  plan  the  streams  and  drainage  lines  as  well  as  the 
directions  of  slopes.  Then  he  sketches  the  position  of  con- 
tour lines  about  such  control  points  as  summits,  salients,  and 
his  own  position.  With  these  as  guides  he  is  then  unable  to 
go  astray  in  the  interpolation  of  the  intermediate  contours 
which  complete  the  map  of  the  area  immediately  about  him. 

The  sketching  of  the  topography  for  large-scale  maps  dif- 
fers rather  in  degree  than  in  kind  from  the  above.  The  large- 
scale  map  covering  as  it  does  a  relatively  small  area,  the  to- 
pographer is  not  under  the  necessity  of  traveling  with  such 
speed  as  to  necessitate  his  using  wheeled  conveyance.  At 
the  same  time  the  largeness  of  the  scale  places  the  roads  at 
much  greater  distances  apart  on  the  map  and  necessitates  his 
traveling  between  these  to  greater  extent.  It  will  thus 
be  seen  that  the  scale  and  the  ability  to  travel  over  the  coun- 
try work  harmoniously  one  with  the  other.  For  the  smaller 
geographic  scales  the  roads  are  so  close  together  on  the  map 
as  to  afford  sufficient  control  and  sufficient  number  of  viewing 
points  for  sketching  the  topography  of  the  average  open 
country,  whereas  on  large-scale  topographic  maps  these 
roads  are  in  plan  much  farther  apart,  but  the  time  consumed 
in  walking  between  them  is  a  comparatively  small  item  be- 
cause of  the  decrease  in  the  distances  to  be  covered. 

In  sketching  a  large-scale  map  the  topographer  will  have 
about  the  same  relative  amount  of  primary  control  as  above 


FIG.  4.— COMPLETED  TOPOGRAPHIC  MAP,  FROSTBURG,  MD. 
Scale  i  to  62,500.     Contour  interval  20  ft. 


SURVEYING    WOODLAND.  33 

indicated.  Starting  out  with  some  known  point  and  on  foot, 
accompanied  by  one  or  more  stadiamen,  he  sets  up  and  ori- 
ents his  plane-table,  and,  having  considerable  areas  to  fill  in 
on  his  map  between  his  present  position  and  his  next  recog- 
nizable natural  feature,  he  posts  the  stadiamen  at  convenient 
changes  in  the  slope  of  the  country  or  at  houses  or  trees  or 
bends  in  the  streams,  and  drawing  direction  lines  and  reading 
distances  by  stadia  to  these  positions  he  obtains  additional 
locations  to  control  the  sketching  (Art.  101),  which  is  exe- 
cuted as  above  described.  In  the  progress  of  this  work  he 
not  only  determines  horizontal  positions  by  sighting  to  the 
rods  held  by  his  stadiamen,  but  also  the  vertical  positions 
of  the  same  points  (Art.  102).  For  very  large-scale  maps 
and  under  some  conditions  the  work  may  be  expedited  by 
permitting  the  assistants  to  sketch  the  contours  immediately 
adjacent  to  their  stadia  stations,  and  these  sketch  notes  must, 
be  given  the  topographer  at  frequent  intervals  to  be  trans- 
ferred to  his  map.  In  this  manner  one  topographer  may 
handle  from  one  to  three  stadiamen,  providing  he  uses  judg- 
ment in  the  selection  of  his  and  their  positions.  For  smaller- 
scale  topographic  mapping  the  work  may  be  expedited  by  the 
stadiamen  riding  on  horseback  from  one  position  to  another, 
or  even  by  the  topographer  himself  using  this  means  to  get 
about. 

14.  Surveying  Woodland  or  Plains. — The  securing  of 
control  in  densely  wooded  country,  as  that  of  the  Adirondack 
region  or  the  woods  of  Minnesota,  Michigan,  and  of  Washing- 
ton ;  or  the  securing  of  control  for  very  flat  plains  country, 
as  that  of  the  Dakotas  and  Nebraska,  is  accomplished  by  dif- 
ferent means  than  must  be  adopted  in  open  triangulation 
country.  Be  the  scale  of  the  resulting  map  large  or  small,  the 
primary  control  may  be  obtained  most  economically  either 
by  triangulation  or  by  traverse  methods.  If  the  country  is 
wooded  and  rolling,  it  may  be  more  economical  to  clear  the 
higher  summits  or  to  erect  high  viewing  scaffolds  upon  them, 


34  SURVEYING  FOR  SMALL-SCALE  MAPS. 

from  which  to  conduct  a  skeleton  plane-table  triangulation. 
Intermediate  positions  may  be  obtained  by  placing  signal- 
flags  in  tall  trees  and  locating  these  by  .intersection  or  using 
them  to  obtain  other  positions  by  resection.  With  prac- 
tice the  topographer  will  thus  triangulate  the  most  forbid- 
ding woods  country  more  expeditiously  than  it  could 
otherwise  be  controlled,  by  taking  advantage  of  every  out- 
look, as  a  rock  on  a  hillside,  a  lake,  a  small  clearing  for  a 
farm,  or  by  clearing  or  signaling  the  commanding  summits. 
He  will  thus  occupy  only  such  points  as  those  just  described, 
locating  by  intersection  (Art.  73)  from  them  the  flags  on  the 
more  wooded  and  forbidding  ones  which  may  be  the  more 
commanding  positions,  and  using  the  latter  again  for  carrying 
on  his  work  by  resection  (Art.  74). 

In  level  plains  or  in  wooded  plateau  land  the  control 
may  of  necessity  be  executed  only  by  traverse  methods.  In 
such  case  where  the  scale  is  of  geographic  dimensions  one  or  two 
astronomic  stations  should  be  determined  (Part  VI),  or  for 
larger  scales  it  may  suffice  to  assume  the  initial  position.  From 
this  primary  traverse  lines  should  be  run  (Art.  226)  at  con- 
siderable distance  one  from  the  other,  depending  upon  the 
scale.  For  the  one-mile  scale  a  nearness  of  fifteen  to  twenty 
miles  will  suffice.  For  the  two-mile  scale  these  primary  traverse 
lines  may  be  double  the  distance  apart ;  for  a  large  topographic 
scale  a  relatively  smaller  distance,  depending  upon  the  map 
scale ;  for  all  scales  a  distance  corresponding  to  fifteen  to 
twenty-five  inches  on  the  map  according  to  the  topography. 

Between  these  primary  traverse  lines  others  of  less  accu- 
racy should  be  run  as  a  secondary  control.  On  these  dis- 
tances should  be  measured  by  wheel  (Art.  98)  when  the 
vehicle  can  be  driven  in  straight  tangents,  by  stadia  (Art. 
101)  in  open  irregular  country,  or  by  chain  (Art.  99)  or  tape 
(Art.  97)  through  underbrush  or  dense  wood.  Elevations 
will  be  secured  in  the  woods  by  vertical  angulation  to  stadia 
(Art.  102)  or  by  spirit-leveling  (Chap.  XV);  in  the  open 


SKETCHING    PLAINS  LAND  35 

or  plains  by  vertical  angulation  to  fixed  objects,  as  the 
eaves  or  chimneys  or  window-sills  of  houses,  the  platforms  of 
windmills,  etc.  (Art.  160),  or  to  the  stadia-rod,  as  well  as  by 
spirit-leveling.  The  secondary  traverse  is  usually  executed 
by  the  party  chief  while  his  assistants  are  engaged  in  tertiary 
traverse  for  the  filling  in  of  topographic  details  or  the  procur- 
ing of  vertical  control. 

The  primary  and  secondary  control  having  been  procured 
as  above,  this  should  be  platted  on  sketch  sheets  of  the  cus- 
tomary large  plane-table  size  for  open  country  (Art.  68),  and 
preferably  in  small  detached  pieces  placed  on  small  boards  of 
about  six  inches  square,  where  the  latter  have  to  be  carried 
through  woods  and  underbrush.  These  control  sheets  will  be 
not  dissimilar  to  those  described  in  Article  13,  excepting  that 
they  will  lack  the  location  of  points  procured  by  angula- 
tion and  will  consist  almost  wholly  of  platted  traverse  lines. 
In  order  that  the  topographer  when  sketching  may  identify 
these  lines  on  the  ground,  trees  must  be  frequently  blazed 
in  woods  when  the  traverses  are  being  run  and  station  num- 
bers or  elevations  be  written  on  the  blazings. 

15.  Sketching  Woodland  or  Plains. — With  the  control 
platted  on  the  sketch  sheet  as  just  described,  the  topographer 
in  plains  work  starts  out  and  drives  over  the  country  much  as 
described  in  Article  1 3 ,  traveling  over  all  the  traversed  roads  and 
checking  his  aneroid  by  setting  in  at  known  elevations  or  by 
angulation  to  and  from  buildings  and  similar  objects.  As  the 
country  is  relatively  flat,  the  contour  lines  are  at  considerable 
distances  apart  in  plan,  and  consequently  a  very  small  differ- 
ence in  vertical  elevation  makes  a  considerable  change  in  the 
horizontal  location  of  a  contour.  Therefore  the  determina- 
tion of  the  vertical  element  should  be  of  greater  relative  accu- 
racy, that  the  resulting  map  may  be  correct. 

In  the  woods  the  sketching  is  executed  in  an  entirely  dif- 
ferent manner.  Little  skill-  is  required  in  the  depiction  of 
the  topography,  as  it  is  impossible  to  see  the  country  and 


30  SURVEYING   FOR   SMALL-SCALE  MAPS. 

therefore  to  sketch  it  in  the  ordinary  sense.  The  topographer 
is  limited  to  sketching  that  which  is  directly  under  foot — in 
other  words,  to  mere  contour  crossings — and  in  order  that 
these  may  be  connected  the  traverses  must  be  much  nearer 
together,  and  not  only  the  topographer  but  his  more  skillful 
assistants  are  all  engaged  in  sketching  and  traversing  at  the 
same  time.  Starting  out  with  the  primary  and  secondary 
control  as  obtained  in  the  last  article,  the  topographer  travels 
over  those  traversed  routes  which  have  been  blazed  and 
sketches  the  contours  upon  these  while  his  assistants  run  addi- 
tional traverses  over  controlling  routes,  as  along  stream  beds 
and  ridge  crests,  and  so  close  together  as  to  completely 
command  all  the  country  under  foot.  These  traverses  will 
be  of  crude  quality,  directions  being  obtained  by  sight  alidade 
(Art.  62)  and  traverse-table  (Art.  61),  and  distances  by  pacing 
(Art.  95)  or  by  dragging  a  light  linen  tape  (Art.  97).  Each 
day  the  topographer  must  adjust  to  his  control  sheet  the 
traverses  with  accompanying  sketching  as  executed  by  his 
assistants.  With  such  a  skeleton  of  topography  on  highest 
and  lowest  lines,  i.e.,  contour  crossings  of  streams  and  ridges, 
he  can  readily  interpolate  contours  for  most  of  the  inter- 
mediate spaces  and,  following  after  his  assistants,  fill  in  those 
places  which  are  not  fully  mapped. 

In  the  execution  of  a  survey  under  such  conditions  the 
topographer's  work  is  largely  supervisory  and  consists  chiefly 
in  the  management  of  the  work  of  his  assistants,  the  adjust- 
ment of  their  sketching,  and  its  inspection  as  he  fills  in  the 
details  omitted  by  them.  There  is  little  room  for  them  to  go 
astray,  because  they  only  sketch  that  which  they  walk  over. 
The  topographer  should  invariably  reserve  for  himself  the 
higher  ridges,  the  ponds,  and  the  more  open  places  in  order 
that  quality  and  speed  may  be  obtained  by  the  utilization  of 
his  skill  in  that  work  which  gives  some  opportunity  for  sketch- 
ing at  a  distance  from  the  traveled  route. 

16.  Control  from  Public  Land  Lines In    the   western 


CONTROL   FROM  PUBLIC  LAND   LINES.  37 

United  States  where  the  public  land  surveys  have  been  exe- 
cuted in  recent  years  and  with  sufficient  accuracy  to  furnish 
horizontal  control,  this  may  come  almost  wholly  from  the 
township  and  section  plats  filed  in  the  United  States  Land 
Office.  The  topographer  takes  into  the  field  paper  on  which 
sections  and  quarter  sections  are  ruled  and  numbered.  On 
these  he  writes  at  the  proper  section  corners  the  elevations 
as  determined  from  the  primary  spirit-levels  (Chap.  XV).  He 
also  indicates  on  the  northern  and  western  margins  of  each 
township  the  offsets  and  fractional  sections  as  shown  on  the 
published  land  plats  (Fig.  5).  At  some  period  during  the 
progress  of  field-work  the  topographer  adjusts  the  land-line 
work  to  positions  determined  either  by  primary  triangulation 
(Chap.  XXV)  or  traverse  (Chap.  XXIII),  supplementing  this 
by  additional  control  where  necessary. 

17.  Sketching  over  Public  Land  Lines. — With  the  con- 
trol sheet  prepared  as  described  in  the  last  article,  the  topog- 
rapher proceeds  to  drive  over  the  section  lines  on  which  roads 
have  been  opened.  The  control  sheet  is  attached  to  a  plane- 
table  board.  Starting  from  a  known  section  corner,  he  drives 
in  a  straight  line  down  one  of  the  section  lines  to  other  sec- 
tion corners,  determining  his  position  by  counting  revolutions 
of  the  wheel  (Art.  98)  and  sketching  contour  crossings  as  he 
progresses. 

Starting  out  with  a  known  elevation  from  spirit-levels 
(Chap.  XV),  he  determines  other  elevations  as  he  proceeds  by 
setting  up  his  plane-table  at  a  section  corner  or  opposite  a 
house  which  he  can  locate  by  odometer  distance,  and  reads 
vertical  angles  from  the  point  of  known  elevation  to  houses, 
windmills,  or  other  objects  in  sight  (Art.  162),  drawing  direc- 
tion lines  to  them  as  an  aid  in  their  identification  (Art.  84). 
Driving  on  until  he  comes  to  one  of  these  objects  and  being 
thus  able  to  locate  it  on  his  plane-table,  he  measures  the  dis- 
tance from  it  to  the  point  from  which  the  angle  was  taken  and 
at  once  computes  his  elevation  (Art.  161).  Or,  setting  up  his 


SURVEYING  FOR  SMALL-SCALE  MAPS. 


^5 


-10 


,•,- 


Hjf- 


FIG.  5.— LAND  SURVEY  CONTROL  FOR  TOPOGRAPHIC  SKETCHING. 

NORTH  DAKOTA. 
Original  scale  2  inches  to  I  mile. 


SKETCHING    OVER   PUBLIC  LAND   LINES.  39 

plane-table  board  from  some  known  position,  as  determined 
from  his  section  lines  and  odometer,  he  reads  vertical  angles  to 
houses  or  windmills,  the  heights  of  which  have  already  been 
determined  by  vertical  angulation,  and  thus  brings  down  to 
his  present  position  an  elevation  by  means  of  the  angle  read 
and  distance  measured  on  his  board.  In  conducting  vertical 
angulation  in  this  manner  care  must  be  taken  to  sight  at  some 
well-defined  point,  as  a  platform  or  top  of  a  windmill,  the 
gable  or  top  of  a  house  or  top  of  door-sill,  etc. 

As  the  sketching  is  a  comparatively  simple  process  under 
these  conditions  because  of  the  flatness  of  the  terrane,  his 
work  may  be  expedited  by  permitting  his  more  skillful  assist- 
ants to  aid  in  sketching.  In  order  that  he  may  control  their 
work  he  drives  and  sketches  over  those  roads  which  parallel 
the  roads  of  his  assistants  on  either  side,  and  in  such  manner 
obtains  a  clear  insight  into  the  work  performed  by  them. 
The  assistants  may  determine  elevations  either  by  vertical 
angulation,  as  does  the  party  chief,  or  by  aneroid  frequently 
checked,  say  at  distances  not  exceeding  tw'o  miles  between 
the  better  elevations  obtained  by  the  topographer.  On  such 
a  sketch  sheet  as  it  comes  from  the  plane-table  board  (Fig.  6) 
the  roads  have  been  clearly  marked  over  the  section  lines  and 
additional  diagonal  roads  have  been  traversed  or  sketched 
directly  on  the  plane-table  board,  controlled  by  section  cor- 
ners, the  outlines  of  lakes  having  been  obtained  by  stadia 
(Art.  101). 

Where  the  topographic  map  is  made  at  the  same  time  as 
the  subdivision  of  the  public  lands,  as  was  the  case  in  the 
Indian  Territory  surveys  of  the  United  States  Geological 
Survey,  the  cost  of  executing  the  topographic  survey  scarcely 
exceeds  the  cost  necessarily  involved  in  making  the  land  sub- 
division or  cadastral  survey.  The  only  additional  cost  in  the 
execution  of  the  topographic  survey  is  that  for  leveling. 
Fig.  33  is  an  example  of  the  cadastral  map  resulting  from 
such  a  survey  of  the  public  lands.  The  topographic  map  of 


40  SURVEYING  FOR  SMALL-SCALE  MAPS. 

the  same  region  corresponds  in  appearance  almost  identically 
with  that  shown  in  Fig.  6,  being  shorn  of  the  various  sym- 
bols used  on  the  Land  Survey  Maps. 

18.  Cost    of   Topographic    Surveys — As    indicated    in 
Tables    I,   II,   and    III,    the   cost   of  topographic   surveying 
varies  widely  with  the  character  of  the  country,  the  scale  of 
the  map,  and  the  contour  interval.     Such  topographic  surveys 
as  are  executed  by  the  United  States  Geological  Survey  range 
in  cost  for  maps  of  a  scale  of  one  mile  to  the  inch  and  2O-foot 
contour  interval,  similar  to  those  described  for  open  country 
in  Articles  12  and  13,  from  $10.00  to  $20.00  per  square  mile. 
Such  as  are  described  in  Articles    14  and   15,  for  plains  or 
woodland,  range  in  price  from  $8.00  to  $12.00  per  square  mile 
for  the  former  to  between  $15.00  and  $30.00  for  the  latter. 
The  highest-priced  work  of  this  kind  which  can  be  executed 
being  the  woodland  survey,  and  the  cheapest  country  to  map 
topographically  being  the  open  plain. 

Land-survey  country,  as  that  instanced  in  Article  16,  which 
is  a  survey  of  a  rJortion  of  North  Dakota,  ranges  in  cost  from 
$5.00  to  $8.00  per  square  mile,  where  the  topographic  map  is 
made  on  a  scale  of  two  miles  to  one  inch  and  in  2O-foot  con- 
tours. For  the  same  scale  and  in  mountainous  country,  as 
that  of  the  South  and  West,  the  cost  is  from  $8.00  to  $12.00 
per  square  mile. 

If  any  endeavor  is  made  to  do  work  for  other  purposes 
than  the  procurement  of  a  topographic  map,  as  for  che  deter- 
mination of  land  lines  or  the  staking  out  of  canals  or  railroads, 
the  cost  of  the  survey  is  at  once  greatly  enhanced.  It  is  this 
which  has  added  so  greatly  to  the  relative  cost  as  shown  in 
the  tables  cited  of  some  private  topographic  surveys  as  well 
as  of  the  cadastral  surveys. 

19.  Art  of  Topographic  Sketching — Mr.  A.  M.  Well- 
ington aptly  said  of  topographic  surveying  that  "  the  sketch- 
ing  of  the    form   of  the  terrane    by   eye    is   truly   an   art  as 
distinguished  from  a  science,  which  latter,  however  difficult  it 


THE  ART  OF   TOPOGRAPHIC  SKETCHING.  43 

may  be,  is  always  susceptible  to  rigorous  and  exact  analysis. 
An  art,  on  the  other  hand,  is  something  which  cannot  be 
taught  by  definite,  fixed  rules  which  must  be  exactly  fol- 
lowed, though  instruction  may  be  given  in  its  general  prin- 
ciples." 

In  representing  the  heights  and  slopes  of  a  given  piece  of 
country  by  contour  lines,  every  case  presents  some  peculiari- 
ties which  must  be  met,  as  they  are  presented,  by  the  topog- 
rapher's own  resources.  No  hard-and-fast  limit  of  minute- 
ness of  detail  can  be  previously  fixed.  The  scale  chosen  for 
the  topographic  map  limits  this  to  a  certain  extent,  but  its 
exact  limits  must  be  set  by  the  topographer's  own  experience 
and  good  judgment,  that  he  may  discriminate  between  impor- 
tant and  trifling  features ;  those  which  are  usual  and  common 
to  the  region  being  mapped,  and  those  which  are  accidental 
or  uncommon,  and  which  should  therefore  be  accentuated. 
Above  all,  the  topographer  must  exhibit  an  alertness  to  dis- 
tinguish as  to  what  amount  of  detail  should  be  omitted  and 
that  which  should  be  included.  Hesitancy  in  this  is  the  chief 
source  of  slow  progress.  Valuable  time  may  be  wasted  in 
the  representation  of  features  which  may  be  lost  on  the  scale 
of  the  work  and  which  are  common  in  all  localities  to  the 
topographic  forms  being  sketched  ;  while  features  characteristic 
of  such  special  topographic  forms  as  those  produced  by  erup- 
tion, erosion,  or  abrasion,  or  those  indicative  of  the  structure 
of  the  region  and  which  give  distinctive  character  to  its  topog- 
raphy, may  be  lost  sight  of  or  be  covered  up  in  the  map  by 
too  careful  attention  to  minute  details. 

The  characteristic  features  of  a  terrane  are  best  observed 
from  a  point  nearly  on  the  same  level ;  and  as  between 
sketching  features  from  above  or  below  for  a  reasonable 
range,  sketching  from  below  is  the  better,  as  features  viewed 
from  any  considerable  height  above  are  apt  to  appear  dwarfed 
and  much  detail  of  undulation  of  the  surface  lost  sight  of. 
Yet,  as  a  precise  representation  of  the  land  requires  sketch- 


44  SURVEYING   fOR   SMALL-SCALE   MAPS. 

ing  its  forms  from  numerous  positions  at  intervals  not  far 
apart,  the  necessity  will  rarely  arise  of  observing  surface 
forms  from  points  of  observation  much  above  or  below  the 
surface  represented,  excepting  in  case  of  very  small  scale 
geographic  or  exploratory  surveys. 

20.  Optical  Illusions  in  Sketching  Topography — In 
sketching  topographic  forms  by  eye  there  are  a  number  of 
optical  illusions  to  which  it  is  well  to  call  attention,  though 
the  effect  of  these  can  be  entirely  overlooked  in  the  sketching 
of  detailed  topography  such  as  would  be  mapped  on  scales 
less  than  one  mile  to  the  inch.  But  for  the  sketching  of 
topographic  maps  on  smaller  scales,  where  the  eye  has  to  be 
more  depended  upon,  these  illusions  become  more  important. 
Most  of  these  have  been  well  classified  by  Mr.  A.  M.  Welling- 
ton in  his  admirable  work  on  railway  location,  and  they  are 
here  summarized,  with  variations,  from  that  work.  Among 
the  more  serious  of  such  illusions  are  the  following: 

1.  The  eye  foreshortens  the  distance  in  an  air  line  and 
materially  exaggerates  the  comparative  length  of  a  lateral  off- 
set so  as  to  greatly  exaggerate  the  loss  of  distance  from  any 
deflection. 

2.  The  eye  exaggerates  the  sharpness  of  projecting  points 
and  spurs,  and  accordingly  exaggerates  the  angles. 

3.  In  looking,  however,  at  smooth  or  gentle  slopes  from 
a  distance,  the  tendency  of  the  eye  is  to  decrease  the  angle  so 
that  in  such  country  as  the   rolling  plains  of  the  West  slopes 
look  much  gentler,  the  inclinations  much  less,  than  they  are  in 
fact. 

4.  In   this   connection   the   eye   is   liable   to   make  slopes 
looked  at  from  a  distance  appear  steeper  and  higher  than  they 
are  in  fact,  when  they  are  compared  with  known  slopes  and 
elevations  of  lesser  dimensions  near  by. 

5.  Again,   the  unaccustomed  eye,  which  mentally  meas- 
ures all  dimensions  by  referring  them  to  those  with  which  it 
is  acquainted,  is  apt  to  make  a  divide  or  pass  appear  lower 


OPTICAL   ILLUSIONS  IN  SKETCHING    TOPOGRAPHY.     45 

than  a  nearer  divide  or  pass  to  which   it  is  referred  in  one 
sweep  of  the  vision,  whereas  it  may  be  higher  (Fig.  7). 


FIG.  7. — OPTICAL  ILLUSION  AS  TO  RELATIVE  HEIGHTS  OF  DIVIDES. 
A  is  nearer  and  lower  than  B. 


6.  The  eye  invariably  exaggerates  the  steepness  of  the  slopes 
of  mountains,  these  appearing  to  have  inclinations  of  from  60 
degrees  to  almost  vertical,  whereas  in  fact  the  steepest  slopes 
are  rarely  as  great  as  45  degrees. 

7.  The  eye  trained  to  estimate  slopes  and  distances  in 
regions  of  large  topographic  features — that  is,  regions  of  ex- 
treme relief  or  differences  of  elevation — will  be  at  a  disadvan- 
tage in  making  similar  estimates  in  a  country  in  which  the 
differences    of    elevation    are    small.      The   tendency   of    one 
accustomed  to  estimating  the  topographic  forms  in  the  Rocky 
Mountains,  where  differences  of  elevation  and  distances  visible 
to  one  sweep  of  the  eye  are  great,  will  be  to   overestimate 
heights  and  distances  in  the  less  rugged  country  of  the  Eastern 
States,  where  great  detail  in  topography  exists,  and  thus  de- 
ceives the  eye  into  an  exaggerated  notion  of  the  amount  of  the 
relief. 

8.  In  viewing  the  terrane  with  an  idea  of  estimating  its 
roughness  as  affording  a  possible  route  for  railways,  canals,  or 
similar  works,  a  rugged  mountain  gorge  with  occasional  pre- 
cipitous narrows,  separated  by  river  flats,  may  appear  much 
more  difficult  and  much  rougher  than  it  is  in  fact.     This  is 
especially  so  as  compared  with  a  gently  undulating  or  rolling 


46  SURVEYING  FOR  SMALL-SCALE   MAPS. 

country,  which,  when  viewed  from  a  distance,  appears  to  be 
comparatively  level,  while  a  nearer  view  will  show  it  to  be  full 
of  elevations  or  depressions  which  will  render  construction 
most  expensive,  because  of  the  rapid  and  numerous  succession 
of  large  cuts  and  fills. 

The  effect  on  the  eye  and  the  mind  is  to  exaggerate  the 
ruggedness  of  a  country  which  is  difficult  to  travel  because  of 
such  impediments  as  broken  stone,  fallen  timber,  creeks,  and 
swamps,  whereas  a  region  where  travel  is  easy  and  free,  as  in 
open  rolling  plains  country  or  where  good  roads  abound,  is 
often  estimated  to  be  much  simpler  and  more  level  topo- 
graphically than  is  the  other  region. 


CHAPTER  III. 
SURVEYING  FOR  DETAILED  OR  SPECIAL  MAPS. 

21.  Topography  for  Railway  Location. — Some  of  the 
worst  errors  in  engineering  location  originate  in  reconnais- 
sance, for  the  reason  that  the  average  reconnaissance  sur- 
veys are  not  of  areas,  but  of  routes  or  lines,  and  there  is  great 
danger  of  serious  error  in  the  selection  of  the  line  to  be  sur- 
veyed. It  may,  accordingly,  be  stated  that  a  railway  recon- 
naissance should  not  be  of  a  line,  but  of  an  area  sufficiently 
wide  on  each  side  of  an  air  line  between  the  fixed  termini  to 
include  the  most  circuitous  routes  connecting  these.  The 
results  of  such  a  survey  should  be  embodied  in  a  topographic 
map  of  greater  or  less  detail,  according  to  the  nature  and  ex- 
tent of  the  country.  If  the  reconnaissance  be  of  a  great  rail- 
road, such  as  some  of  the  Pacific  roads,  built  through  hun- 
dreds of  miles  of  unknown  country  the  resulting  map  should 
be  on  a  small  scale,  perhaps  2  to  4  miles  to  the  inch,  and 
with  contour  intervals  varying  from  20  to  100  or  200  feet, 
according  to  the  differences  of  elevation  encountered  and  the 
probable  positions  of  several  locations.  With  such  maps  as 
those  of  the  U.  S.  Geological  Survey,  the  number  of  possible 
routes  may  be  reduced  to  two  or  three,  and  a  more  detailed 
topographic  survey  should  then  be  made  of  these  on  which  to 
plan  the  final  location. 

As  ordinarily  practiced,  topographic  surveys  for  railways 
are  made  by  the  older  methods,  with  transit  and  chain  or 
stadia  and  with  spirit-level ;  notes  of  the  surveys  are  kept  with 
accompanying  sketches  in  note-books,  and  these  are  reduced 
to  map  form  in  the  office.  The  same  results  can  be  much 

47 


48         SURVEYING  FOR  DETAILED    OR   SPECIAL   MAPS. 

more  satisfactorily  and  more  rapidly  procured  by  using  the 
plane-table  in  place  of  the  transit,  and  the  resulting  map, 
being  plotted  in  the  field,  is  a  more  accurate  and  available 
representation  of  the  terrane  than  can  possibly  be  made  from 
plotting  notes  in  an  office. 

The  Germans,  who  are  very  thorough  in  taking  topography 
for  railroads,  divide  the  work  into  three  separate  surveys  of 
different  degrees  of  accuracy :  first,  recourse  is  had  to  the 
government  topographic  maps  on  a  scale  of  approximately 
i:  100,000,  and  on  this  a  preliminary  route  or  routes  are  laid 
down :  second,  a  more  detailed  topographic  survey  is  made  in 
the  field  on  a  scale  of  1 : 2500  as  a  maximum  or  i :  10,000  as 
a  minimum,  with  contour  lines  of  15  feet  interval.  This  map 
is  limited  in  area  from  a  few  yards  to  a  few  hundred  yards  in 
width,  according  to  the  nature  of  the  country.  Where  no 
previous  small-scale  topographic  survey  exists,  the  base 
of  this  more  detailed  or  second  survey  is  a  transit  (Art.  87) 
or  plane-table  (Art.  83)  and  level  (Art.  129)  traverse,  follow- 
ing as  nearly  as  possible  the  approximate  route  of  the  pro- 
posed railway.  Bench-marks  (Art.  135)  are  established  along 
this  at  distances  of  from  500  to  1000  feet,  by  which  the  ane- 
roid may  be  checked.  With  this  transit  line  completed  on 
the  proper  scale,  the  topographer  goes  over  the  ground  and, 
by  means  of  distances  from  pacing  (Art.  95)  or  odometer 
(Art.  98),  and  elevations  by  aneroid  (Art.  176),  constructs  a 
hasty  contour  map  on  which  are  indicated  all  roads,  water- 
courses, structures,  high-water  marks  of  bridges,  width  and 
height  of  existing  bridges  and  culverts ;  and  all  other  necessary 
topographic  details  as  to  the  position  of  rock  masses,  strike 
and  dip  of  strata,  swamps,  springs,  quarries,  etc. 

On  such  a  map  as  this,  hastily  and  cheaply  made,  it  is 
possible  to  plan  the  detailed  topographic  map,  limited  from  a 
few  yards  to  100  or  200  yards  in  width  and  covering  what 
will  practically  be  the  final  route  of  the  located  line  as 
obtained  from  the  second  survey.  This  final  detailed  survey. 


DETAILED    TOPOGRAPHIC  SURVEYS.  49 

from  which  the  paper  location  is  to  be  taken,  should  be  on 
a  scale  of  from  1:500  up  to  I  :  1000  and  with  contours  of 
about  5  feet  interval,  more  or  less,  according  to  the  nature 
of  the  land.  There  is  plotted  on  the  plane-table  sheet  the 
transit  and  level  base  line  previously  run  for  the  second 
survey,  and  the  instruments  now  used  by  the  topographer  are 
of  a  more  accurate  nature,  consisting  of  a  plane-table  (Arts. 
58  and  83)  for  direction  and  mapping,  two  or  more  stadia 
rodmen  for  distances  (Art.  102),  while  elevations  are  had 
by  vertical  angles  with  the  alidade  (Art.  59).  On  this  final 
map  are  shown  much  the  same  topographic  details  as  on  the 
second,  but  all  are  more  accurately  located  and  the  eleva- 
tions are  of  a  more  refined  nature.  The  data  furnished  by 
this  final  map  will  serve  all  the  purposes  of  making  a  last 
paper  location  of  the  line,  from  which  the  engineer  will  in 
the  field  possibly  deviate  according  to  the  appearance  of  the 
route  traveled  as  presented  to  his  eye  when  the  location  is 
laid  down. 

Mr.  Wellington's  location  of  the  Jalapa  branch  of  the 
Mexican  Central  Railway  (Fig.  8)  is  an  excellent  example  of 
a  detailed  contour  topographic  map  for  railway  location. 
This  was  platted  in  the  field  on  the  scale  of  I  :  1000,  or  about 
83^  feet  to  i  inch.  The  contour  interval  was  2  meters,  or 
6.56  feet. 

22.  Detailed  Topographic  Surveys  for  Railway  Loca- 
tion— Prior  to  making  the  location,  which  may  be  made  in 
part  from  the  notes  of  preliminary  surveys,  a  narrow  belt  of 
topography  should  be  mapped  in  detail,  its  width  being  re- 
stricted as  far  as  possible,  providing  the  preliminaries  have 
been  skillfully  conducted  or  have  been  preceded  by  a  small- 
scale  topographic  map  executed  with  especial  care  along  the 
possible  routes  of  the  location  (Art.  21).  On  the  detailed 
topographic  map  a  paper  location  may  be  made,  from  which 
full  notes  of  the  alignment  can  be  derived,  the  points  of  curve 
and  tangent  taken  off,  and  a  profile  of  the  paper  location  pre- 


SURVEYING  FOR  DETAILED    OR   SPECIAL   MAPS. 


DETAILED    TOPOGRAPHIC  SURVEYS.  5  I 

pared,  For  the  making  of  the  paper  location  the  topography 
should  be  as  exact  and  the  contour  lines  should  be  as  accu- 
rately placed  as  the  scale  of  the  map  will  permit,  in  order  that 
a  line  may  be  located  upon  the  map  and  a  profile  called  off 
from  it  which  shall  agree  as  closely,  as  possible  with  the  sub- 
sequent transit  location  and  spirit-level  profile.  In  running 
the  field  location  from  a  paper  location,  the  projected  profile 
and  not  the  projected  alignment  must  be  run. 

In  making  such  a  map  it  is  neither  necessary  nor  possible 
to  locate  every  point  on  each  contour,  the  horizontal  and  ver- 
tical locations  of  the  contours  being  at  such  distances  apart 
that  their  projections  on  the  map  will  be  so  close  together 
that  in  connecting  them  by  eye  in  the  field  the  topographer 
cannot  go  astray  by  an  appreciable  distance.  With  a  detailed 
contour  map  made  as  described  for  the  location  of  canals  (Art. 
23),  a  grade  contour  or  location  line  may  be  drawn  which  will 
show  where  the  plane  of  the  roadbed  will  cut  the  natural  sur- 
face and  from  which  it  will  at  once  be  seen  whether  or  not  the 
location  is  the  most  favorable  the  topography  will  permit. 

The  error  into  which  many  have  fallen  is  in  assuming  too 
much  or  too  little  for  the  topography  as  a  guide  to  location. 
The  topographic  map  fails  to  show  many  essentials  requisite 
in  making  a  location,  as  it  gives  no  evidence  of  the  materials 
to  be  encountered,  nor  does  it  convey  an  adequate  idea  of  the 
magnitude  of  the  excavations  and  fills.  The  topographic 
map  must  be  supplemented  by  a  careful  visual  reconnaissance 
of  the  line  which  it  covers.  Such  topography  should  there- 
fore be  restricted  in  its  width  and  amount,  and  no  attempt 
should  be  made  to  make  a  final  location  from  such  a  map.  On 
the  other  hand,  where  a  topographic  map  is  not  made,  and  too 
much  reliance  is  placed  on  the  visual  reconnaissance  of  the 
country,  the  greatest  errors  are  at  once  introduced  in  encoun- 
tering a  bad  system  of  gradients,  in  overlooking  important 
towns,  or  in  otherwise  selecting  inappropriate  routes. 


52        SURVEYING   FOR   DETAILED    OR   SPECIAL    MAPS. 

In  planning  the  location  on  a  detailed  topographic  map, 
the  engineer  should  begin  at  a  summit  or  similar  fixed  point, 
assuming  or  taking  from  a  guide-map  an  initial  elevation. 
Then  with  a  pair  of  dividers  he  should  step  off  such  distances 
that  these  will  correspond  to  the  grade  chosen  and  their 
termini  end  on  the  map  above  or  below  such  contours  as  will 
give  the  proper  differences  in  elevation  to  produce  such  grades. 
By  this  means  a  grade  contour  can  be  sketched  in  on  the  map 
and  then  connected  by  tangent  lines.  The  latter  must,  in 
turn,  be  connected  by  throwing  in  curves  the  radii  of  which 
shall  be  as  large  as  possible,  care  being  taken  that  the  grades 
on  these  shall  be  properly  compensated.  With  such  a  paper 
location  it  is  then  possible,  by  means  of  scale  and  protractor, 
to  take  off  the  directions  and  distances  in  a  note-book,  when, 
with  these  as  a  guide,  the  located  line  may  be  run  on  the 
ground  and  changed  or  modified  in  the  field  as  the  visual 
observation  of  the  engineer  may  suggest. 

Speed  in  mapping  railway  topography  varies  greatly  with 
the  scale  selected  and  the  character  of  the  land  mapped. 
One  party  working  in  flat,  desert  country  in  Utah  ran  20 
linear  miles  in  a  day  of  9  hours,  including  running  of  spirit- 
levels.  The  same  party  working  later  in  mountainous  country 
in  Washington  averaged  during  a  long  period  of  time  less  than 
\  mile  a  day,  in  one  instance  working  six  weeks  on  a  location 
through  i£  miles  of  canyon.  A  party  working  on  railway 
location  and  mapping  topography  on  the  plains  of  Kansas 
made  an  average  speed  of  2.1  miles  a  day  at  an  average  cost, 
including  all  expenses,  of  $i  1.03  per  linear  mile.  The  Utah 
work  averaged  about  $2.50  per  mile,  and  the  cost  of  much  of 
the  Washington  work  exceeded  $100.00  per  linear  mile. 

23.  Topographic  Survey  for  Canal  Location. — Surveys 
for  canal  lines  or  lines  of  conduits,  etc. ,  are  best  made  by  having 
the  leveling  (Chap.  XV)  precede  the  plane-table  or  transit 
work.  The  level  will  then  run  out  a  grade  contour  having  the 
requisite  fall  per  mile,  and  the  transit  (Art.  87)  or  plane-table 


TOPOGRAPHIC  SURVEY  FOR    CANAL   LOCATION.          53 

(Art.  83)  with  chain  measurements  (Art.  99)  will  follow  the 
level,  locating  this  grade  contour.  Topography  may  be 
taken  on  either  side  by  stadia  (Art.  101)  and  plane-table  so 
that  in  the  final  location  of  the  canal  the  preliminary  grade 
contour  may  be  shifted  to  suit  the  sketched  topography, 
much  as  the  line  of  a  railway  location  would  be  shifted  from 
similar  data  (Art.  22). 

An  interesting  example  of  a  detailed  topographic  survey 
for  the  final  location  of  an  irrigation  canal  is  that  made  by  Mr. 
J.  B.  Lippincott  of  the  Santa  Ana  Canal,  through  a  rocky  can- 
yon. This  location  was  made  upon  a  carefully  prepared 
topographic  map  drawn  on  a  scale  of  50  feet  to  I  inch,  with 
contour  interval  of  5  feet.  The  maps  were  plotted  from  cross- 
section  notes  based  on  two  connected  and  approximately  par- 
allel preliminary  lines,  the  contour  curves  being  sketched  in  the 
field  to  indicate  intervening  irregularities  of  surface.  The 
preliminary  controlling  lines  were  carefully  run  with  transit 
and  chain,  were  frequently  connected,  and  had  a  vertical  in- 
terval of  70  feet.  The  space  between  and  for  thirty  feet 
above  the  upper  line,  or  for  a  total  of  100  feet  vertically,  was 
carefully  contoured.  From  the  map  thus  prepared  a  more 
accurate  cross-sectioning  was  made,  and  from  these  notes  a 
new  contour  map  of  the  ground  was  prepared  on  a  scale  of  30 
feet  to  an  inch  over  the  more  difficult  portions  of  the  line, 
after  a  preliminary  location  had  been  selected  on  the  first  con- 
tour map.  Fig.  9  gives  a  plat  of  one  of  the  roughest  por- 
tions of  this  line,  and  on  it  are  shown  in  small  circles  the 
various  points  located  on  each  contour.  The  plane-table  was 
used  and  was  set  up  generally  as  shown  by  the  station  num- 
bers and  triangles  on  the  preliminary  and  plotted  traverses, 
and  directions  were  measured  to  stadia-rods  held  at  various 
points  on  the  lo-foot  contour  lines  (Art.  101).  The  posi- 
tions of  the  contour  lines  at  these  points  were  therefore 
plotted,  and  the  corresponding  elevations  were  immediately 
connected  as  contour  lines  on  the  plane-table  sheet.  In  this 


54          SURVEYING  FOR  DETAILED    OR   SPECIAL   MAPS. 


TOPOGRAPHIC  SURVEY  FOR    CANAL   LOCATION.          5$ 

way  enough  points  were  located  on  each  contour  to  sufficiently 
control  it,  and  the  immediate  2-foot  contour  lines  were  in- 
terpolated by  eye  estimation  in  the  field. 

In  doing  this  work  three  various  methods  were  tried :  (i)f 
by  locating  the  contour  lines  with  slope-board  and  rod ;  (2), 
by  locating  the  contours  at  right  angles  to  the  stations  occu- 
pied by  a  levelman  using  a  hand-level  (Art.  156);  and  (3), 
by  means  of  the  plane-table  and  stadia  (Art.  101).  Mr.  Lip- 
pincott  says  that  as  a  result  of  these  tests  there  is  no  question 
between  the  quality  of  the  three  classes  of  work ;  that  without 
plane-table  the  work  had  to  be  plotted  up  in  office  and  located 
points  connected  by  estimation  or  from  rough  sketches;  with 
the  plane-table  the  same  points  were  plotted  immediately, 
in  the  field,  and  the  connections  between  these  made  with  the 
terrane  in  view,  and  that  the  resulting  map  by  plane-table 
much  more  accurately  expressed  the  slopes  of  the  land  than 
did  the  maps  made  by  the  other  methods.  The  speed  by  the 
various  methods  was  about  the  same.  The  party  consisted 
generally  of  five  persons,  including  the  topographer,  levelman, 
and  rodman,  and  the  speed  was  from  2500  to  4000  linear  feet 
per  day,  actually  locating  four  lO-foot  contours  and  sketching 
in  five  or  six-  more,  a  total  of  100  feet  vertical  interval,  and 
interpolating  the  2-foot  contours.  Where  side  canyons  and 
ravines  were  passed  the  slope-board  was  found  to  be  entirely 
inadequate  and  helpless,  while  by  the  use  of  levelman  and 
hand-level  without  the  plane-table,  and  with  taped  traverse 
lines,  the  conditions  were  improved,  but  the  work  was  of 
the  crudest  character  so  far  as  its  topographic  expression  was 
concerned. 

An  example  of  a  preliminary  topographic  survey  of  a 
canal  line,  made  under  the  author  with  plane-table  and  on  a 
small  scale  to  determine  the  possibility  of  bringing  the  water 
from  a  stream  or  reservoir  to  certain  lands  for  purposes  of 
irrigation,  is  illustrated  in  Fig.  10.  The  scale  of  this  illus- 
tration is  denoted  by  the  land  section  lines,  each  section 


SURVEYING   FOR   DETAILED    OR   SPECIAL   MAPS. 


\ 


SURVEYS  FOR   RESERVOIRS.  57 

being  a  mile  on  a  side.  The  original  survey  was  made  on 
a  scale  of  3000  feet  to  the  inch,  with  a  contour  interval  of  4 
feet.  The  plane-table  was  accompanied  by  a  spirit-level  to 
determine  grade,  in  order  that  the  canal  line  might  be  given 
the  required  fall  per  mile. 

24.  Surveys  for  Reservoirs. — In  making  surveys  of 
reservoirs  for  storage  of  water  for  city  water-supply  or  for 
irrigation  and  similar  purposes,  the  scale  and  contour  interval 
depend  necessarily  on  the  dimensions  of  the  reservoir.  The 
former  should  be  from  400  to  1000  feet  to  the  inch,  and  the 
latter  from  2  to  5  feet  vertical  interval.  Special  surveys 
should  be  made  of  possible  sites  for  dams  and  waste-weirs  on 
larger  scales  and  with  a  contour  interval  of  I  or  2  feet,  and 
several  cross-sections  of  the  dam  site  should  be  run  and  the 
topography  taken  in  detail  for  a  sufficient  distance  above  and 
below  the  center  line.  If  sufficient  borings  or  trial-pits  are 
sunk,  a  contour  map  of  the  foundation  material  may  be 
constructed. 

Perhaps  the  most  satisfactory  manner  of  making  surveys 
of  reservoir  sites  is  instanced  in  the  following  practical  ex- 
ample of  one  made  by  the  author.  A  standard  or  base 
transit  (Art.  87)  and  level  (Art.  129)  line  is  first  run  across 
the  dam  site,  carrying  the  same  a  little  above  the  highest 
possible  flow  line  of  the  reservoir.  From  this  should  start  a 
main  transit  and  level  line  which  should  follow  up  the  lowest 
or  drainage  line  of  the  reservoir  basin  (Fig.  11,  A,  Dt  G), 
and  this  should  be  extended  until  it  reaches  an  elevation 
corresponding  to  that  of  the  highest  probable  flow  line  of  the 
dam.  Bench-marks  (Art.  135)  should  be  left  as  this  line 
progresses,  and  stadia  distances  measured  (Art.  102),  and  level 
elevations  taken  to  points  within  the  range  of  the  level-tele- 
scope, as  at  A,  B,  etc.  Based  on  this  main  transit  and  level 
line,  a  plane-table  and  stadia  line  (Art.  101),  accompanied  by 
spirit-leveling,  should  be  run  from  the  highest  flow  line  of 
the  dam  cross-section  around  the  corresponding  contour  line 


ffini    - 


58        SURVEYING   FOR   DETAILED    OR   SPECIAL   MAPS. 

on  one  side  of  the  reservoir,  H,  /, /,  etc.,  and  if  the  land 
be  clear,  stadia  and  level  sights  may  be'  taken  to  the  other 
contour  lines  within  the  range  of  the  instrument,  including 
sights  on  lines  of  equal  elevation  on  the  opposite  side  of  the 
reservoir  if  the  latter  be  small.  If  large,  however,  a  number 
of  flags  may  be  located  on  the  opposite  side  by  triangulation 
(Art.  73)  or  by  stadia  observations,  and  cross-section  lines  be 
run  to  these,  from  which  the  data  for  constructing  a  contour 
topographic  map  can  be  obtained  as  at  /  and  L. 

Another  example  of  a  reservoir  survey  is  illustrated  in 
Fig.  12,  which  is  a  portion  of  the  map  of  the  Jerome  Park 
reservoir  site  in  the  city  of  New  York,  and  was  platted  on  a 
scale  of  400  feet  to  the  inch  with  a  contour  interval  of  10  feet. 
From  such  a  map  it  is  possible  to  compute  the  contents  of  a 
reservoir  for  each  additional  five  feet  of  elevation,  and  on  it 
land  lines  and  property  lines  are  shown  in  such  manner  as  to 
indicate  the  damage  which  will  be  done  by  submergence. 

25.  Survey  of  Dam  Site. — A  typical  illustration  of  the 
topographic  map  resulting  from  the  survey  of  a  site  for  a 
dam  for  closing  a  storage  reservoir  is  shown  in  Fig.  13. 
This  survey  was  executed  with  a  plane-table  (Art.  73),  chain 
(Art.  99),  and  spirit-level  (Art.  129)  on  a  field  scale  of  400 
feet  to  I  inch,  with  a  contour  interval  of  2  feet.  The  result 
of  such  a  topographic  survey  is  to  indicate  clearly  the  best 
alignment  for  the  dam,  providing  the  borings  which  must 
necessarily  follow  the  selection  of  such  alignment  prove  its 
feasibility. 

An  example  of  a  topographic  survey  executed  for  selec- 
tion of  a  site  for  a  weir  or  diversion  dam  in  a  river  is  that 
illustrated  in  PI.  III.  This  shows  the  topography  of  the  flood- 
bed  of  the  Snake  River  between  its  high  bluff  banks,  as 
well  as  the  contouring  of  the  bed  of  the  river  as  shown  by 
soundings.  On  this  is  indicated  the  best  alignment  for  the 
diversion  weir  as  well  as  for  the  canal  head  and  headworks. 
The  field  work  of  the  survey  was  executed  with  transit. 


